Any lag in Versus mode can be a result of any number of things, but likely it is a connection issue. Since you are connecting to another player somewhere else in the world, depending on where they are, there could be a significant amount of Fight Rollback, meaning the game is regularly trying to keep you two in-sync.
I'd recommend adjusting you're frame delay to see if that helps, you can adjust that in the Settings during team select before you search for a match. This should help the match flow a bit better if you're often experiencing lag.