This will only work after you have found the burial chamber --
So how do I actually find the burial chamber?
-- gotten into the upper room --
How do I get into the room I can see above the pillars?
-- and overheard an argument from that location. Don't read on until those things have happened.
After you ask Lily about the argument, she'll give you a chore. Do it and then come talk to her again.
How do I arrange the amulets for Lily?
You'll now have the option to tell her that Abdullah wants to talk to her. She'll immediately run off to talk to him, and the residence tent is yours.
Lily will also be gone briefly if you ask Dylan to distract her.