You've earned it, so we're going to let you in on a little secret of novel writing. Ready? Sometimes characters exist just to propel the plot along. When you have a lot of central characters with big emotions and important thoughts, you somehow have to corral them together and force them to bump against each other—and an easy way to do that is to have some slighter, less important people around to sort of buffet them into action, like a dog herding sheep. In The Idiot, Lebedev is pretty often that dog that gets things moving.
Think about how many times Myshkin only gets a piece of information because Lebedev happens to bust into his room and annoyingly tell him about it. Or, even better, how many times we find out that Lebedev has been scheming something behind someone's back. (Which again is usually a plot detail revealed by Lebedev himself.) And, even more tellingly, how strange a coincidence it is that Lebedev just happens to not only own a house, but also rent out a room right in the middle of where all the action is? Sometimes it's just convenient for an author to have a go-to guy.