My Dane would be happy to try to sit in your lap and he usually doesn’t fart.
Funny you mention it that. Had another friend who raised Great Danes. They seem to think they’re still lapdogs - no idea of their size. Ufff. But if a passenger had a Great Dane and was next to me on a plane, I’d be happy to have him/her sit on my lap. They really are in general very gentle giants.
Now I’d find my sneezing for the next few days to be annoying (I’m alergic), but it would be worth it.