I'm looking for a relic, which I have to give to the lich. Unfortunately I cannot find the relic, I can't even find the door, which I can open with the lich's key. Can anyone help me?

From where you enter Skull castle head for the stairs in the room to the right going down. You enter a series of three rooms - they are pretty open to one another, there is a pool of water on the upper level and south of it on the lower level is a gate that you can open with the lich's key.
Have fun!

Wyv