I know some people on another site who have lhasa and they are perfectly fine with other dogs. One of the has one with two shih tzus and they all get on fanstastic with no problmes at all. As others have mentioned they are not any more snappy than any other breeds, i know a lot of small breeds have this hanging over them. Shih Tzus for one and Charlie couldnt be less snappy if he tried.
I just want to mention leaving a smaller dog with a bigger one, although accidents can happen i know somebody with 3 Shih Tzus and a great dane (what a mix! ) lol and she says they never have any problems, i think dogs if they are brought up around other dogs or well socialized then they kinda figure how to play with other breeds big or small! Charlie isn't sizest at all and will quite happily play with other Tzu sized dog or a golden lab......he isn't fussy lol
Good luck on your search and let us know what you decide on
Oh and there is a Lhasa owner on here some where, Abbeys_mommy i think her name is her pup is called Abbey and she has the cutest picture with a dummy (pacifier) in her mouth lol so maybe she will come by and tell you a bit more on the breed! I know she posted on any shih tzu owners in teh toy group section.
Sharon and Charlie