All breeds have their standards even in character, but they are individuals, and as such will be different. Lhasa Apsos are breed standard laid back and non aggressive, but supposed to be suspicious of strangers - mine wasn't.
A shitzu Also a tibetan breed but small and friendly, and not madcap energetic, and look very cute. They do need coat clipping to keep in a puppy style as their coats are very long and thick otherwise - look gorgeous as a show dog. Or a Lhasa Apso, similar with similar coat needs, even more laid back.
we have got 2 tibetan terriers, an older bitch and an almost 2 yr old male and they have very different personalities. the bitch is fear aggressive toward other dogs and is very serious, she doesnt do cuddles or playing with toys (she was a rescue) the male is a proper clown, VERY intelligent and quick to learn but they are not mindlessly obedient, its like they are asking 'whats in it for me?' when you give them a command. the male is quite dominant with other dogs, hes like a big baby who doesnt understand boundaries. their coats take a lot of looking after as well, best to have a puppy clip if you arent going to show - my mum shows the male and he has to have a bath and full groom every 5 days or so which takes 3-4 hours at a time. they also suffer terribly with seperation anxiety as a breed. ours arent particuarly good with children, they dont like to be petted by them but that could just be our dogs not being used to them, we dont know any small children. i wouldnt reccommend them as first dogs, they can be very hard work but they are very rewarding. theres not a nasty bone in the males body and our girl would never dream of ever biting a person, they.just dont seek affection the way other dogs might