Can I invite myself to a lab to give a talk?

There's absolutely nothing wrong with making an outreach to a group you're interested in learning more about. Just make sure not to make it too hard of a sell: you could say something like, "I'd like to visit your group, and I could give a talk if you'd like." I don't think most professors would be put off by such a request.

It is usually hard for institutes to find external speakers (and expensive to invite), so anyone willing to visit at their own expense is warmly welcomed. In particular if the institute has a (semi)-recurring seminar series to fill with speakers.