Yes, Zug would be the right place for Landtwing.
If the person is still alive, you won't be able to get a cert, I'm afraid. If s/he is deceased, you can contact the local register office (explaining your relationship to the person) and ask for information.
zivilstandsamt [at] zug.zg.ch
If you understand French, there's a short article about the family here:
http://www.hls-dhs-dss.ch/textes/f/F25387.phpIt might be worth trying a Swiss genealogy forum - I don't know whether there's a site for Zug genealogy society, but I'll look when I get back from the school run...
Rambler