Is asking someone out via email lame?

I've read a few previously asked questions/answers about this topic but hope to get a few opinions on my particular situation? I have one class with him, which meets every other day. It's a large pit lecture, so sometimes I see him and sometimes I don't. We recently worked on a project for this class together (how I actually met him) and other than maybe an hour of face-time we really only communicated about it via email. Usually when I do see him, he's with a friend (who, coincidentally enough, I am currently doing a project for class with) and the possibility of getting turned down in front of another guy deters me from approaching and asking. The other problems? I have no idea if he has a girlfriend, nor do I have his phone number so calling is out.

If asking him through email would be ok, any suggestions on how to do so without seeming like a total tool? Do I ask about the girlfriend thing or just ask to 'meet up' and assume that if he has one he'll make that known??