Ok, after rewatching it I'm rather sure that the driver IS Lelouch. You have to look at C.C while she is talking. When she says "Right, Lelouch?" she raises her voice and her eyes go up like she is trying to look behind her, which is the direction the driver is sitting.
I might have gotten crazy but that's how the scene is looking to me, don't shoot me^^
Gotta watch the episode myself, when I get it, but that's so how I would imagine it. Thanks for the interpretation, awesome