Do you have a more suspicions player to suggest be lynched at the moment? Who could actually be lynched?
Do you think two days worth of no-lynches is productive?
They might have an usual condition to acquire them at first though, but after that they'd be present in game, and probably randomly jump around to a new player after they were used.
After what I did to him Day 1, he would want to eliminate me because otherwise I'd be on his case for the entire rest of the game. Especially since he knows he isn't Town.