The Drunken Lizard Pub

I wasn't sure whether to put this here or in the support forum, but since this this isn't exactly a bug, I put it here.

So on my first character, I felt that I didn't make him how I wanted to, so I decided to start over. In the main quest I got to the point where Lilith gives you the quest to kill the Queen Bee.

On my second character, I decided after I got the amulet from the crypt that I would do some misc. quests and power up first. I did the quest where you carry the crucible from Bordertown to Blackwater. Upon reaching Blackwater, I found a house containing a corpse and a note...well you see where this is going if you've played through the game. First there was the shady guy that asks you to kill Lilith, which was pretty weird O_O. After getting the Crux of Ages and reading the note, I thought 'ok cool I skipped ahead a bit'. But upon returning to Lilith's house, I found that she can't give you the quest to clear out the Hive.

Will this quest re-activate if I still complete it? Or is every quest between Lilith's and getting the Crux of Ages gone for good?

Based on what you've just said, I think you are fine. When you got the Crux, a note should have told you what to do next. At this point you don't need to visit Lilith at all.