Equipped with the key. Go to the Eastern door shown in the above screenshot (watch out for new spawns. Enter a new dig location in which you will have to solve another puzzle connected with the newly acquired skill.
Go through the big bridge. But stop and look around, more or less, after you reach its central point. Initiate the Soul Split. While controlling the first half of the soul, use the death grip. I spoke shown in the above screenshot. Using the interactive agents reach a balcony to the south. Stay on the balcony for a moment and acquire Arbiter Scroll (You only need to approach the symbols appearing on one of the walls).
[TIP: if at the moment of solving the puzzle, you unexpectedly return to physical form, this will mean that one of the halves of the soul strayed too far away from the petrified death. Should such a situation occur make sure that you activated soul split while in the middle of the bridge.]
Find some other interactive ledges that you can hold onto, shimmy as far right as you can and in the spot shown in the above screenshot, start climbing in. Jo vertical wall run bounce off from walls. This way you will reach the upper balcony.
Once there, start searching for another Book of the Dead Page (side quest [The Book of the Dead]). No, you can approach the mechanism shown in the above screenshot. Interact with it and using it turn the bridge by 90° (the one with the physical form of the dead on it).
Switch now to the other half of the soul, but remember to us to hold the E key down at all times, because it's important to keep the bridge in that position, at all times. Go to the newly opened northern part of the area (the above screenshot).
For starters. Find a Boatman Coin and a chest. Find the narrow corridor all and reach the switch shown in the above screenshot. Using the switch will result in unlocking access to the lantern, but you cannot take it with you.
Continue controlling the other heart for the soul as you return towards the rotated bridge. Look around for the interactive creeper in the location shown in the above screenshot, and use it to reach the upper balcony. Once all of the balcony, use Death Grip in order to land on the neighbouring ledge, and peek inside the last chest has been in this part of the dungeon.
Terminate soul split and return to the central area of the city of the dead. Explore the North eastern corner and use Death Grip in order to catch the above-mentioned lantern (the above screenshot).