Who would win in a battle between Yog-Sothoth and The Living Tribunal?
Living Tribunal has been killed previously, thus he is obviously less powerful. He was rewritten to be considered the embodiment of the Marvel Multiverse. Yog-Sothoth is one step higher, Yog-Sothoth is all space and time, thus Yog-Sothoth is reality itself. Yog-Sothoth could remove the Living Tribunal from existence with a thought.
Yog Sothoth exists at all points in space and time at once. This extends into infinite universes and dimensions. Powerful as the Living Tribunal is, his existence is tied to the Marvel Multiverse so he has limitations whereas Yog Sothoth doesn't. It's doubtful Yog Sothoth would consider the Living Tribunal a real threat but if he truly felt the need to act, he could simply change history and prevent the creation of the Marvel Multiverse. This would retroactively wipe the Living Tribunal from existence.
The Living Tribunal in a MAJOR stomp here.
I dont know what Justin or James know but as a Cthulhu/Marvel fan im sorry but Azathoth or Yog-Sothoth OR anyone else is not touching the Living Tribunal you would need ACTUAL Omnipotence to damage/kill The Living Tribunal.
All Outer Gods exist outside of the Omniverse like The-One-Above-All (though they are below TOAA by definition (though it is possible that Azathoth *is* TOAA)), whereas The Living Tribunal is 'merely' infinite dimensional in nature. There's a reason the Cthulhu Mythos is considered one of the most powerful fictions in existence, with the only 'verse I can think of with such a concentration of Outer God level entities being I/O.