I've finally managed to solo Elite Zawabi's Revenge (ADQ2/DQ2/DQ) on my clonk, so I thought I'd share some of what I've learned. Much of this knowledge wasn't figured out by me, I'm standing on the shoulders of giants as it were.
This should work for any divine, probably any WF Arcane, and possibly Pale Masters. Some Melee's can solo this raid, usually via high AC (60+ for normal, higher on other difficulties), but that is outside the scope of these tactics.
If anyone has any extra info that is useful, I'll edit it into this doc, so please leave suggestions. In particular, I've only done this on a divine, so arcanes may have extra tricks.
Primary strategy: Laser Turtle.
The key to this method of killing the DQ is to apply Damage over Time spells, and then simply survive. Shield blocking is very effective as the raid involves lots of hits for low damage, and much of that damage is alignment based. One large reason this tactic works is because her strikes follow certain patterns. If you learn the patterns, you can minimize how often the DQ hits you while you're not blocking. Timing well means you'll only get hit by archers and efreets while you cast heal. Time poorly and she'll hit you with 18+ attacks and, depending on your alignment and HPs, possibly take you from over half to dead.
The only real required feat is Quicken. Although as survival is key, Toughness(es) and Shield Mastery are also very useful.
Other than quicken, probably the most important part of your build is your alignment. Damage from the archers is pure evil. Damage from the DQ is Unholy, Anarchic and True Chaos. Put it all together, and:
LG: bonus 1d6 from archers, 5d6! from each DQ strike (and she hits rather quickly)
NG: 1d6 from archers, 3d6 from DQ
CG: 1d6 from archers, 2d6 from DQ
LN: 1d6 from archers, 3d6 from DQ
TN: 1d6 from archers, 1d6 from DQ
CN: 1d6 from archers
Note... when you see exploits of crazed solo casters/divines on the DDO boards that are CN... this is probably why. Other than the ability to use stability gear, I'm not sure if there are any other advantages of being TN over CN.
Maximize/Empower are good just to shorten the fight. The shorter it is, the less chance there is for you to make a mistake.
The other key part of your build is your Red Bar. You will take damage. Lots of it. The more of a beating you can take between heals the better. Healing Amp would be useful mainly to boost the RS Aura, or FvS capstone heals.
That said... I've managed Elite now, and I'm LG. Build wise, I have a 14 base con (ate a +2 tome as well), 1 Toughness feat, and Shield Mastery. With LG you may need all that... although I bet it can be done without Shield Mastery depending on gear. For other alignments, it will be easier for you than it was for me.
It is all about survivability. You may need some sort of mana regen (Con Opp or Torc), but I'm pretty sure normal can be done without. Worst case scenario, pots can fill that gap. Better damage (potency, brilliance, lore, etc) helps by reducing how long you need to go with no mistakes.
Things that help you survive....
DR: I recommend 5 DR from something. Via crafting it isn't hard to simply create an Axeblock and a Spearblock item. You can get 5 DR with one item via the Bloodrage Symbiont or some of the named armors/shields. The symbiont is a bit of a gamble though. I've had it break during my attempts. It survives most of the time though if you have an Adamant ritual on it (its what I used). On the off chance you have them, Bramblecasters are nice for the greater spearblock (10 DR).
Shield: The main quality you want here is blocking DR. You'll be shield blocking whenever you aren't casting. Shield blocking not only gives that extra DR, but it prevents overrun, and most importantly, it prevents the extra alignment damage. Note, an Arcane can craft themselves Arcane Casting Dex gloves that will, I believe, completely negate the Arcane failure from a Mithral large shield. Another random note... you may need to Adamant Ritual your shield as well, at least for higher difficulties. With hard I found that to be an issue with my Madstone Shield.
Healing/False life guards: Demonic Shield is the best, and is available from the Anniversary event platemail, or from Bracers of the Demon Consort. Life Shield is also available, but only is worth about 1.5 damage per hit vs. the 5 or so from Demonic Shield. I've found Demonic Shield to be more useful than evasion, so far hard and elite I suited up my CC armor and pretty much lost all clonkiness.
Other guards: You're getting beat on like mad, so they'll process plenty. I imagine regular guards aren't really worthwhile (although the Acid one will probably do a touch of damage), but the various end game guards (such as the shroud ones) should help. I find the Mabar cloaks invis guard useful for confusing the minions for a bit. A stoneskin guard make work as a DR replacement, but would probably be better in addition to, rather than replacing one.
Spell boost clickies: Superior Brilliance 5 (must be crafted) and Superior Ardor 6 or the arcane equivalents. Not key, but they help some. Even if you have a potency item, these boost your Divine Punishment or Aura/Heal 75% instead of potency's 50%.
Elemental resists: There will be fire, acid, electric and sonic attacks. I don't think there is any cold attacks... but once I'm buffing the 4, I just do all 5 to be sure.
DeathPact: This is hard to use... but I found a way. Be sure you are wearing a Featherfall item. When you get killed, run over to the 2 O'Clock position and jump off. Raise yourself, and immediately Heal yourself, and recast Fire Resist. Land on the ledge, and proceed to rebuff anything else you want. Catch your breath, and go back in. Be sure to go back in blocking, as you don't want to get overrun. If the DQ is right in the center.... you'll probably be overrun regardless. It isn't perfect, but I think it gave me a valid second chance 80% of the time. (The rest I either landed in lava, or got overrun as soon as I ported back up.)
Shield/Nightshield: she casts missles sometimes
Divine Power: not really key, but blocking DR is influenced by BAB, which can be boosted with Divine Power.
Anything that helps saves is also useful. Heroism/GH, Prayer, Holy Aura, Pro Evil, etc.
FvS Archon: any extra DPS helps
A decent Summon: I like the Eladrin Ghaele from Summon 9 the best. The summon won't really do anything except distract the enemy. The Ghaele seems to be the longest living summon.
Blur/Displacement: It won't matter vs the DQ, but I'm pretty sure it will help vs her minions.
RS Aura: Anything that can heal you while you are still blocking is great. It is basically more DR. When the DQ is on the platform, it is probably all you need.
Basic: Hit her with DoTs and block. For Divines, obviously Divine Punishment is the only game in town. For Arcanes, Acid DoTs are ideal, with fire/cold behind. According to ddowiki, she's immune to lightning, and has resistance to fire/cold depending on difficulty.
Port in. Kill all of the Efreet & Mephits. I just melee them down, but I imagine most divines would be better doing a BB kite. DP would work as well, or anything else you normally use.
After you go through the portal, I do a summon before shrining. Save as much mana as possible (although with a Torc, my blue bar really doesn't move much). You can actually port in right next to the DQ before you finish your buffing. Nothing will happen until you talk to her.
Talk to her. Block while you are clicking the answer, as it will start as soon as the last one finishes. If you stand too close you'll get overrun before she ports away.
Then go to the edge of the platform facing the DQ. Hit her with your DoTs and block. When the DoTs are off of timer, hit them again. When she comes down, turn to face her, and continue that process. When HPs get low (possibly 30-50%, depending on your bar), heal yourself. I keep a Cure Crit hotbarred next to my Heal for when I need to heal but the Heal itself is still on cooldown. Eventually she'll port back up. You can use that opportunity to recast any short buffs (Ardor, Brilliance, DP, Aura, maybe even a new summon, etc....). Keep the DoTs going though, as you'll otherwise lose the stacking damage.
It will take a couple of times of that, but the strategy stays the same. Eventually she'll Rage... but really nothing changes other than everything gets harder.
The real key is to learn timing. She has a few different strikes she can take (including a triple strike which hits for 18+ attacks) but by watching her closely you can largely time your heals to minimize her hitting you when you're not blocking. You need to heal yourself with enough HPs to withstand the efreet and archers while you unblock to heal yourself though, so be careful. One way to learn her timing is to practice on ADQ1. She uses the same basic attack patterns, but on casual, she doesn't do that much damage in ADQ1.
I found the biggest problem of the efreets was they could obscure my view of Lailat. Some people bother to kill them and the archers, but I didn't find that too necessary. The damage they did while I was shield blocking was effectively zero, although they did force me to heal myself when I had more HPs that I would have if I was vs. Lailat alone.
I'm curious if anyone else has any luck with this. I think DQ is now probably the easiest raid for a divine to solo. Supposedly Reavers was... but I think the seemingly more plentify Air Elementals changed that (combined with how well DP/shield blocking works on DQ).