I made it to that room and opened the chest. I broke open the lock on the door and got what I guess is the Death Wand. The lich never appeared when I came into the room though - only way to get the key?

Are you in the right room dude?? The lich doesn't leave his room (ie the one down the stairs - before you follow around to the tipping bridge). You get the key to his room from the altar with all the death head spells (one of 4 directions you can swim after being tipped from the bridge into the water). Where exactly are you at Sroutt?

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Welcome to the board, sroutt!!!

Sounds like you're in the Lich's study which isn't where he is to be found. He's in his music room which from the entrance is:
go up small flight of stairs and use wing latch to open gate
enter a large room with many ghosts and two stairways at the back leading to one exit
through that exit - the next stairs down lead to the Lich.

To get the key to open that door you need to go to the tilting bridge, fall into the water and take the northwest most passage/tunnel out which leads you to a room full of traps. On the far side of the room the key is sitting on a table. You may have to jump onto the table to actually get the key.

Good luck!!

Wyv