No, stages have nothing to do with it twesterm. Riot and I played on Hyrule Temple (second biggest in the game) and it was completely lag free, and my friend and I have played on Mushroomy Kingdom at least 3 times lag free (it's a sidescroller).
There are only 2 reasons you will ever experience lag in Brawl:
1) The internet connection of one of the players involved blows
2) The players are a very large distance apart.
For 2 it has to be larger than the distance from Indiana to California (since I played that distance lag free), which is over 2,000 miles, so I mean VERY large.








