I noticed there was only one real guide for playing LA R'lyeh, and it was an MA/LA guide
(see here) whose LA advice was basically: "Play LA R'lyeh like MA R'lyeh, and take growth to mitigate your dominion's dreamlands effect." Its a good MA guide, and some parts of it (like the early game synopsis, and Baalz post in the thread about R'lyeh as a submarine, for examples) are still relevant, at least to degrees, to LA R'lyeh, but burning 120 design points to mitigate the dreamlands seems wasteful, and otherwise trying to play LA R'lyeh like MA R'lyeh is probably not optimal.
Table of Contents
1. The Dreamlands as a strategic asset
2. Scales
3. Pretender Design
4. Units: Micromanagement Hell
5. Commanders
6. Research
7. Some Additional Strategy Notes
1 - The Dreamlands as a strategic asset
As LA R'lyeh, your dominion is toxic. You will kill off your population amazingly quickly. While this will impact your income and supplies, it will also make taking lands that you have held for any length of time a poor proposition because they simply aren't worthwhile for other nations anymore. This is an advantage - fighting LA R'lyeh is like fighting an opponent with a scorched earth defensive policy, leaving nothing for the invaders. Furthermore, enemy armies that enter your dominion will see their commanders slowly go mad and begin behaving erratically. Pushing your dominion into your opponents' lands will reduce their assets and drive commanders even outside of your borders to madness. The dreamlands is your first line of defense against invasion and an offensive weapon against your neighbors.
2 - Scales
Since spreading your dominion will also spread your scales, you want to choose scales that maximize the toxicity of your dominion.
Death 3 is an obvious first step - since you've already accepted that your population is going to die, they might as well die faster. Its 120 basically free points. (And its not like your starspawn have to worry about old age).
Sloth 3 is even more obvious for LA than MA R'lyeh. Most turns you will only ever purchase a commander in any given territory.
Cold 3 is another obvious choice. You will be mostly unaffected underwater, and your water evocations will benefit on land.
Turmoil 3 and Luck 3 are an advantageous combination for you. On the one hand, your income from holding provinces is going to be poor. There are, however, a large number of events which will give you additional cash. These include the relatively common 100-300 tax, temple donation, and similar events, and scale up to the 1000-3000 gold events. This is an important source of income that doesn't care what your population is, just how many provinces you have (more chances at events).
Good events will also supplement your gem income, which is even more important to you than your cash income in a lot of ways.
Magic 0 is perfectly acceptable - you'll be buying a large number of mage commanders. Anything higher than Magic 1 is unnecessary.
3 - Pretender Design
So, our preferred scales are Tu3 Sl3 De3 Co3 Lk3 Mg0 for the reasons given above. This nets us a massive 360 extra points for our pretender.
Regardless of what chassis you ultimately decide on, the first thing you're going to do is increase your Dominion to 10. Spreading the dreamlands as far and as fast as possible is to your advantage.
R'lyeh has no early bless strategy. Our only purchaseable sacred unit is the priestly Starspawn, who is not immune to insanity and therefore of limited use to us (for the void gate, generally). All our void creatures are sacred, but their availability is unpredictable at best and as such they won't be able to be fielded in any numbers until the mid or late game. At best, a moderate rainbow bless is all we're going to want out of our pretender for this.
We are going to care immensely about our gem income though, which suggests an Awake Rainbow pretender for manual site searching. Despite being aquatic only, I prefer the archmage. With a little bit of air he'll be able to forge himself an amulet of the fish to get onto land later, and has easy access to new paths of magic while having a low chassis cost. A lich or master lich could also work, but the chassis will eat a substantial number of points.
You should definitely prioritize at least N1 so you can find underwater fortifications - they're common and will multiply the number of Starspawn mages you can buy, given cash. A1 will let you make an amulet of the fish if you need it. While you can send out some of your mages to help with site searching, i find having water and astral on your pretender makes your site searching more efficient (although forgoing astral and doing that remotely is certainly an option). Ultimately, having every (non-blood) type of magic in the 1-4 range will help you find a large number of sites quickly and ramp your gem income up. Since Blood is really hard to get into underwater (can't bloodhunt in sea and ocean provinces), it may be best to skip it (although having blood on your pretender can allow you to use bloodhunting for crafting purposes in the midgame - for example, making Robes of the Magi is certainly not a bad idea).
4 - Units: Micromanagement Hell
This is usually the place where a guide writer reviews all your units available for purchase and makes recommendations. Instead, I have a simple analysis: ignore every single non-commander unit you have for purchase. Ok, you'll buy some in the first few turns for early expansion, and the MA/LA guide is perfectly adequate at covering that. But after your second army is out the gates, don't bother.
Reason number 1 is the freespawn. You will get ridiculously large numbers of them. You will need commander units to ferry all these freespawn around and get them to the front so you can sacrifice them en masse. Armies of 500+ units are not implausible. This is, however, micromanagement hell. But you will need to manage the freespawn because they do cost upkeep, and the more of them you can get killed the less of them you have to pay for.
Reason number 2 is you need every available penny for commanders and upkeep. Your battles will be hordes of freespawn backed up by mages and summoned creatures. Having sufficient mages to maintain research and run your armies is critical.
Your freespawn come in a few varieties. Underwater they can use multiple chassises (merman, deep one, triton), and on land they tend to be human or hybrids. They can be Dreamers (regular troop) with good morale and daggers, or Mad Ones (magic troop) with no weapon and unbreakable morale (50!). Additionally, creatures MA R'lyeh can only void gate summon will sometimes appear as freespawn in your provinces, possibly effected by high luck and local dominion strength. These can include such gems as Formless Spawn and Greater Otherness, but I have not observed a Vastness that freespawned yet.
Yes, i know illithids are good. No, you can't afford to keep 50 gold troops around. Get over it (or go play MA R'lyeh where you can enjoy your illithids).
5 - Commanders
Starspawn Mage: 280/1 W1S3 +2 @100% WESD +1 @10% WESD
This is almost where discussion about purchased commanders stops and ends. As your only commander unit (other than your god) who is immune to insanity, these are immensely valuable not only for their spellcasting ability, but for their ability to be able to act every turn as you desire. Many of your freespawn are also magical creatures, so your mages will make decent battlefield commanders as well. They come in a number of distinct flavors, so lets review the most useful ones.
W1E2S3: Your best dry land battle mages, they can cast Summon Earth's Power -> Gift from the Heavens without boosters, and slapping crystal shields and/or rings of wizardry on them will make them even more efficient. Empowering to 1N will give them Eagle Eye, and 1F will give them Magma Eruption.
You'll also want to empower one of these to E3 (can't wear boots, but you'll have the earth gems) so you can make early hammers to help reduce forging costs, especially for astral crafts. This same mage can later be boosted into casting Forge of the Ancients with a RoWizardry and an Elemental Staff.
W1S3D2: Capable of Skelly Spam and some value as artillery support with nether darts. Not the most useful, but useful enough. If you want undead chaffe summons they can provide, although given how much chaffe you have available this is only useful on the front lines to replace losses if you're having logistics issues getting your freespawn there in time, so if/when you capture a laboratory you might make use of this capability.
W1E1S3D1: good as a communion slave to a mixed master pool, or with a crystal shield capable of being versatile between the previous two set ups. You'll put many of these on research duty, but a few as additional support mages scattered across your armies won't go too far wrong.
W3S3: Good summoner early on with pretty decent battlefield evocations once you get spells like ice strike.
W1S5: Good forgers for high level astral crafts (like RoW) and Mindhunters.
Starspawn Priest: 150/1 S1H2 +1 @100% WESD
Unlike their Mage brethren, they are not immune to insanity. However they do come with some Summoner skill, and so are useful for entering the void gate and calling creatures. You probably won't want to buy one until you get Thaum 1 for Returning so you can save him from attacks and getting lost in time and space. (S2 can cast it naturally, S1X1 can cast Power of the Spheres first). Since insanity and getting Lost in T+S will make them inactive for various time periods, eventually having 2 to keep the void gate active is probably a good idea, but this is not a priority.
Starchild: 85/1 S1 stealthy
Despite being prone to insanity, they're a cheap communion slave option and available for purchase at coastal fortresses. You might buy some.
Illithid Lord: 80/39
With 40/40 magical/normal leadership, they're a good chassis for moving troops around. Unfortunately, they do go insane. But they're cheaper than designating mages for ferrying duty.
Slave Mage: 175/1 W2S1 +1 @100%WESN
They can go insane, they aren't that much more efficient than your starspawn at researching (certainly not once you factor in turns lost to insanity), and they lose power on land. However, they do get a chance at nature. Empowering a W2S1N1 to W3 will let them forge clams and summon a Naiad, so you might consider trying for one with a nature pick (although empowering a 3W3S starspawn to 1N will allow the same and is superior, but you're less likely to see a 3W starspawn early. Alternately, if you can spare your pretender from site searching he may be able to summon a Naiad with the right magic paths).
Cultist: H1 +1 @?% S
Freespawn commanders (also available for purchase in coastal forts), they come in two flavors. The underwater one is amphibious and looks like a deepspawn. The land one is human-looking. Both are priests and can have astral magic. Only the land version is purchaseable, although you're unlikely to want to do so. They start insane, and will often take actions like become prophet (even if you have one), allowing you to have many H3 priests. Useful against nations like Ermor who rely on their undead, and for blessing your void troops. Since they can freespawn just about anywhere, they're also useful for ferrying troops around (admittedly without the best magical leadership).
None of the other commanders are even worth considering, and most of the ones discussed above have primarily niche uses. The backbone of your nation is your starspawn mages.
6 - Research
Conjuration 2 is a good early priority because it will let you start eating your water gems summoning a few early sea serpents to quickly dominate any nearby ocean.
Thaum 1 will give you returning for your void gate summoner.
After those Evocation 4 provides Gift from the Heavens (among other useful spells), Enchant 2 allows for skelly spam, Construction 2+ will allow you to start forging things like clams and hammers (with a little empowerment here and there), and Alteration 3 will open up Ethereal Body and the like. More Conjuration is also desirable because your only real access to good troops is summoning them, and you'll have the gem income to do so. Enough Thaumaturgy to get spells like teleport and gateway is also an excellent idea. How you prioritize these is subject to personal preference and what your local opposition looks like - evocation is less useful in an underwater war (with say a nearby Atlantis), whereas it will be critical for any serious land expansion.
Your emphasis on purchasing lots of high quality mages puts you in good position to dominate the research game, so you have a good shot at getting unique summons like the elemental rulers first, or getting your choice of global enchantments - and you'll have the gem income to do either. Once you get the necessary early research done, you may consider focusing your efforts on one of these two goals.
You have a unique commander summon at Conj 6: Contact Void Spectre. Absolutely any Starspawn Mage can cast this spell, and it gives you an ethereal undead starspawn commander who is stealthy, has S4, and causes insanity in the province he's in. Summoning and infiltrating large numbers of these can be a great way to get a dreamlands-like effect deep in enemy territory, improve your information advantage, and possibly quickly capture lightly defended territories. Sitting one or more of these on your opponents' research centers will eventually cause him to lose a lot of research/crafting/ritual casting time, and he may not even think to check and see if they've gained an insanity score. And between astral buffs and some half-way decent gear they can solo typical levels of PD.
7 - Some Additional Strategy Notes
The first thing to note is that LA R'lyeh retains all the magical strength of MA R'lyeh, so the MA/LA guide is a good place to start for this. Mindhunting, information advantage via scrying, using R'lyeh as a 'submarine' (see Baalz response in the MA/LA guide), and more are still excellent ideas. In fact, you're likely to have even more mages than an MA R'lyeh player would.
The challenge with LA R'lyeh will be capitalizing on your two strengths, both of which will require lots of micromanagement. You will have a large number of powerful mages to use, and a large number of weak but steadfast troops scattered across your provinces.
You will have exceptional gem income, especially in N, W, and S with decent E and D. Don't be afraid to use your N gems to empower some battle mages - Eagle Eyes will be quite useful in getting the most out of your evocation spells. Churning out 10-20 mages worth of summons (like Wolves of Winter) in one turn is also a fairly effective way to build a decent midgame upkeep-free army from scratch.
Do put some mages on forge duty. Crystal Shields, Robes of Invulnerability, Rings of Wizardry, and other gear to protect and enhance your mages are all excellent ideas, and you can afford them in numbers to kit out your battlemages.
I like to turn my initial scout into a prophet and use him to search for holy sites - underwater temples are a common feature with S gem income.
Steer clear of summons which will cost you gold in upkeep. You will need to support a heavy upkeep burden without willfully taking on Troll summons or the like, don't make it worse than it already is.