"The only thing you are going to see, is the burning hand of overdue justice." - Lobster Johnson
“There are only three forms of high art: the symphony, the illustrated children's book and the board game.” - Saga
Unless I missed something, I believe the team still has to take time in the Rest Phase if Lobster Johnson is knocked out. LJ wakes up and rolls dice to heal like other agents.
This is how the rules sound to me. I think his ability only shines during the confrontation. Yo have the last Last-Ditch Recovery and Lobsters ability to bring him back.
His ability would be better, if it would trigger at the start of the Agent Phase and not in the End Phase.