We host karaoke every third Wednesday at the Loft after the English comedy nights, see here:
Lausanne Karaoke Nights
The next event is 14 October at 10.15p.

Otherwise, Café des Artistes in Galerie Saint-François has karaoke every night except Sunday and Monday, I think. Beware that their book could be much better and some hosts are not the most cheerful sort.