Lich's Soul

You must be at least 7th level and have completed Morgiah's quest to be offered this quest. The summons will usually arrive as soon as you finish distributing your attribute points upon reaching 7th level. If the messenger arrives before you are 7th level, save the game and rest for about 6 hours and you will level.

The King of Worms will send you a letter via UPS (Undead Postal Service). After killing the delivery zombie, you'll find the letter stitched into it. The King of Worms wants you to run an errand for him. If you don't come quickly, you can count on his zombie reminder service to keep the matter fresh on your mind (this handy reminder feature was a bug that was fixed by one of the later patches, so if you don't get your daily reminder, don't sweat it)

Go to Scourg Barrow and down to the King's office (taking potshots at the liches and vapires if it makes you happy). He'll tell you that there's a lich haunting the Castle Sentinel dungeon and he wants you to soul trap it. Your reward? Information.

You enter Sentinel Castle just as you did to take up Lhotun's Quest. He's still sitting there if you want to wave on your way to the dungeon.
Go out the back door of the Grand Hall and to the back door on the north wall. You will find an elevator there that will take you up to the throne room.
Go through the first opening on the right (south) wall and through the door at the end. At the end of this passage is another elevator. Use it.
After a long walk down a seemingly endless corridor, take the first opening on the left wall and then the first passageway on the right wall (don't go through any doors). You will run into three human critters on your way.
Go through the door at the end and follow the passage to an elevator. Go up and get off at the first opening. Pull the lever you find in the room at the end, then take the elevator all of the way up to the top.
The lever lifted a set of blue bars blocking a doorway. Go across the room and take the elevator on the other side (it's the only unblocked doorway) all the way to the bottom.
DO NOT pull the lever by the elevator. Instead, go around the corner and take that elevator to the SECOND opening.
Kill the Spider and take the elevator to the top.
Go east from the top until you get to a lever. Pull it. Now go back to the elevator and north, across the room and take the elevator down to the bottom.
Deal with the Ghost and pull the lever you find in the room at the end of the passageway.
Take the elevator back up to the top, go across the room and take the elevator back down, past the spider, and down the bottom corridor again.
The blue bars are gone and you can deal with the Wraith (if you didn't take care of him earlier). Pull the lever and ride the elevator all the way to the top.
The doorway is now open and you can go deal with the Lich. Remember that you need Mithril or better weapons to hit him. If you wait at the corner, you can shoot him through the wall. The exit will be directly across from you when you come back to the room at the top.

Assuming that your bones aren't keeping the lich company, go back to the King of Worms. He'll tell you about the Battlemage who helped the first emperor conquer Tamriel and was later betrayed by the emperor. The Battlemage eventually became the Underking. The King of Worms cautions you about what could happen if Zurin Arctus (the Underking) ever gets his mortal body back. You'll get a magical something-or-other for your troubles and you've gained a few brownie points with the King of Worms (now isn't that special?).