I know to use "live" for plural and "lives" for singular. I was just asking whether it should be singular or plural in the sentence. Your first reply makes me think it depends on what is meant. e.g. if I think "they" all are thinking the same, or have the same opinion, then I should say "I can't read their mind". But if I think each of them has his own thoughts, then I may be better to say "I can't read their minds"? But I don't remember ever seeing such use "their minds".