It occurred to me the other day that at least three of the four "corners" of the house of troubles has some connection to Lorkhan, or did in some variant of the lore. Sheogorath may have had origins relating to Lorkhan's defeat (the "Sithis-shaped hole") while Malacath, as Trinimac, was the one who slew him. Mehrunes Dagon was the Leaper Demon King, and conspired with Lorkhan to cheat Alduin. If there's a connection between Lorkhan and Molag Bal, I'm not aware of it.

I have no idea where I'm going with this, but I thought I'd put it out there and see if it provoked any thoughts.

My thoughts:

Trinimac-Malacath: Those who witnessed the Tower-splitting of Lorkhan-Those who changed due to this changing force and got influenced by Lorkhan: Divine Path Recycle, Death and Rebirth, Mundusism

Wonder if this theory can be linked to the path of CHIM and Amaranth

Jyggalag-Sheogorath: Those who bored and avoided by Lorkhan-Those who inspired and being inspired by Lorkhan: Divine Motivation Madness

Leaper Demon King-Mehrunes Dagon: Those who confronted Aka-Those who got doomed by Aka: Divine Result (pro-anti)Creation

Linked to Lorkhan by Aka

Molag Bal-Molag Bal: Those who represented absolute rulership-Those who uneffected by Lorkhan: Divine Rivality Enantiomorph

Overlapped greatly to Aka and thus linked to Lorkhan