Infiltrating the Immaculates is part of the main storyline in Divinity: Original Sin. Most of this quest is fairly straightforward, but at the later stages you may encounter two hard to spot objects you will need to progress further.
Once you reach Mangoth in the underground Immaculates temple, you will first need to open a trap door next to the altar where Mangoth disappears from.
To open the door, use the lever displayed on the screenshot above.
Next step is to take a path in front of the altar that just opened up.
In this room, you need to active four switches, but in a particular order:
Switch #1:
Switch #2:
Switch #3:
Switch #4:
After pressing the four switches, the door to the central room will open in the south side. Once you approach it, you will be ambushed by Mangoth and several of his minions, so be prepared.
Once you defeat Mangoth and his elementals, loot the Vial of Leandra’s Blood and Leandra’s Diary, and go to your Homestead to talk to Icara to combine Vial of Leandra’s Blood with Leandra’s Spell (obtained during Investigating the Mines quest).
Lastly, talk to Icara to finish the Infiltrating The Immaculates quest.