You should just need to talk to Dotharhar (hallway by specimen room) about the book borrowed from the library to trigger the speech option with Tax to get the key. Try talking with him (again?) and then Tax...
If you still can not get the key, there are a couple workarounds. You can get a replacement key (
Inventory files) or bypass the locked door (by
hex teleporting or
using a summoning doll).
