Thought I'd take a break from slapping little kids around and do some constructive analysis.
Living Tribunal vs. Classic Beyonder.
Ok, I understand that 'Classic Beyonder' refers to your state of mind when you think of the Beyonder...to properly participate in this discussion, you have to believe he was as powerful as depicted before his retcon.
With that in mind, you have to find a spot for him in the food chain, and it is surely near the top.
From what I remember he had insane reality warping abilities, he pushed around the Celestials, and 'killed' Death. I would place him at a level above Eternity and Death...but I didn't see anything that would suggest that he could eclipse LT.
In the multiverse controlled by LT, I would probably place him second.
LT can shut down an entire universe...BUT, he apparently has no jurisdiction in Beyonder's realm, so that presents a problem. Here's where the questions come into play.
How much raw power does LT possess? Just because he has no jurisdiction, does that mean he is physically unable to subdue the Beyonder? We will never know.
Considering we don't know, it's best to go on what we've seen. So strictly based on assumption, I would say the Beyonder would probably win. For the simple reason that he is in his realm, LT is outside of his. Sort of how Mephisto is uber powerful in his own realm, but considerably weaker outside.