It depends on what you mean by "lost their medical." If you know you have a condition that would keep you from passing your next medical, so you let the old one expire and don't try to get a new one, your driver's license will let you fly LSAs. (There are, however, rules against flying if you know you have a condition that would disqualify you, though they are obviously hard to enforce.) But, as NorfolkSouthern has pointed out repeatedly, if you failed your last medical exam, or if your last medical was suspended or revoked, your driver's license will not be enough to let you fly LSAs. The only way to recover from that kind of thing is to pass a third-class medical exam.