I was doing quests in Athkatla the other day and suddenly realized there was stuff in the underdark I didn't do. So I backtracked my way through the caverns inhabited by countless (they respawned every other minute) Kuo-toa and some beholders. The drow had left their city gate wide open so I waltzed in and killed them all. Almost. There's this one house that I need some kind of wardstone to enter. I obviously don't have the said wardstone and I'm asking whether it is to be found on one of the inhabitants, or is it some sort of plot device I would have, had I bothered to do all sidequests when I was there the first time?

Also, What's behind those locked doors in the tavern? Can I still open them after killing everyone?

Also also, any tips or superior strategies for killing the lich?

The wardstone is indeed from a (very good!) quest you receive in the Drow city. I won't spoil you, but it is connected with the Drow who offers you the "magical rope" that protects you from the Lich (he's on the bridge near the lich's house). It is a quest reward unfortunately, so you won't find it lying on a corpse.

The tavern does not have any locked doors at all, unless you mean the gates to the gladiator pits. If you didn't fight there, too late, you missed your chances(s). The Temple of Lolth has a couple of locked doors, but those will become unlocked if you do all the quests. The Wardstone for the House Jae'llat can be gained only by tangling with Deirex--and be careful, it will only work once.

Deirex is only difficult if you have Tactics's Smarter Mages installed: He's very close to the entrance when you go in, he's quite likely to blow off 2x Horrid Wiltings the instant you see him, and his tower is a party-required area, so you've got to expose your entire party to that. Just Reload until he randomly picks something else to be in his "Enemy Sighted" contingency, and then deal with him as you would any other Lich.

I have the rope, yes, but the lich is causing me some trouble. No tactics or anything, I just can't kill liches. I think there are two or so in all games I have started that I destroyed without abusing the rules in some way. They just seem to be immune to about anything.

Iron Greasel, Lichs are imune to spells level 1-5, so, spells like breach won't remove their spell protections. I find Ruby Ray of Reversal (Lvl 7) is a great spell for removing Lich protections. Also make sure your Mage/Cleric casts true Sight.