The Souls have to be obtained in a strict order, so for starters go through the newly unlocked west door (the above screen). Cross over the bridge and enter the first chamber.
Inside you'll find a Lich which is going to summon Skeletons for assistance. I strongly recommend focusing on the Lich, though, since he'll never run out of his "monster reserve". Try to run him into a corner using special attacks. Once the Lich is dead, his minions will also be gone.
Proceed forth. Go through several narrow corridors and enter a hall with a summoning circle. Naturally, use Interdiction and take your helper to the adjoining room. Send the Dead Lord over the pressure plate in front of you (the above screen).
Go across the newly created drawbridge and send your helper to another pressure plate, in the eastern part of the hall (the above screen).
As you may have noticed, only one half of the drawbridge has been lifted. Stand on that part and select Death Grip. Now, jump towards the Dead Lord standing on the pressure plate, and pull yourself to him by pressing the middle mouse button.
Once you're at the new shelf, look around for a shadowbomb and throw it at the yellow formation close-by. This will lift the other half of the drawbridge.
While you're there, look around for a chest hiding a Dungeon Map. Afterwards, face the lantern pictured on the above screen and catch it with Death Grip. With it, go to the statue in the central part of the hall and attach it to it (E button).
When it's done, rotate the statue. First, turn it towards the southern part of the chamber to unlock access to the chest shown on the above screen.
Now, rotate the statue towards the door in the northern part of the chamber. But that's not all - you also have to send the Dead Lord over to a pressure plate directly in front of it (the above screen). Only then will you be able to leave the hall.
Head north, reaching an oval tower room with a demolished staircase. For starters, I suggest diving to find a Relic of Khagoth underwater (the [Lost Relics] side quest). Surface afterwards.
Move up the wall where shown. After reaching the top interactive edge, lean back and jump, grabbing onto an interactive handhold in flight (remember to have Death Grip active).
Holding onto the top edge, start moving left. Lean back again and jump backwards, BUT don't use Death Grip at the moment - instead, let the character land on a nearby shelf. You'll find a chest there (the above screen). Jump down to a yet another shelf to find a second chest.
Now you have to go back to the interactive edge mentioned above. Again, lean back and jump, but this time do use Death Grip to grab onto it (the above screen).
Wait for Death to reach the top interactive edge. Lean back for the last time and jump. You can now approach the first Lost Soul and press E to take it (the above screen).
Unfortunately, taking the Soul leads to a battle which is made additionally uncomfortable given the small size of the battlefield. You'll be pitted against a Lich and Skeletal Champions. I recommend eliminating the Champions first, especially since you can easily block their attacks with Death Grip while exposing them to your strikes at the same. Watch out for the Lich in the meantime, as well as his summoned Skeletons (area-effect attacks advised). Attack the Lich only after all the Champions are dead.