Yeah we could go into the what ifs and the butterfly effect of putting these players on the Flyers and taking them away from their actual realistic teams (creating all sorts of different and alternate outcomes).
But let's not try to dwell TOO deep into all of that and keep it lighthearted, I mean it can be fun to think of what would happen to the other team without the "lifer", maybe they never become a dynasty, maybe their team has to move, maybe they get a crack at a different superstar in the draft instead......make it FUN to think of the aftermath of the player being on the Flyers!!!
If by lifer you mean a player that has or had played their whole career with one team, then I think I'd have to go with Martin Brodeur... Blasphemous answer, I know, but I picked Brodeur mainly because I'd have likely seen a couple cups in my lifetime so far.
I was thinking of Chris Pronger, but thats not what the OP was asking.
I guess I would go with Patrick Roy.
Roy played for two teams so he was never a lifer, neither was Bourque (as per OP's example).
Hands down I would have to say Marty. Not only did we, and many other teams, pass on him in the draft, having a consistent record-setting goalie would be the best thing to happen to this team since he was drafted. Followed by Yzerman - great leader, player, and GM.