If you've eaten anything made with lobster stock in a restaurant, you've eaten dead lobsters, which are called "stiffs" are are available from every seafood wholesaler.
I wouldn't serve the meat on its own, but I wouldn't think twice about making stock with it. In my most recent lobster bisque adventure, my fish guy suggested going this route and using frozen Atlantic tails for the meat, but he just didn't have any stiffs to sell me.
I wouldn't go there. I grew up on the coastand was always taught you only cook live crabs. I would use that rule for lobster too. I was taught shellfish can turn bad quicker than almost anything and the resulting illness is quite unpleasant.
I bought some lobster tales at a market one time and as soon as I got them home and opened the wrapper the ammonia smell hit me and I tossed them. I guessed they were from lobsters that had died in the tank.
If he thinks it's okay, than ask him to give you one to try it