I don't think Lanny Davis negotiated anything on behalf of Cohen. In fact, Davis isn't even a "real" lawyer at all. He's a political operative, and the only reason for Cohen to have him on his legal team is so Davis can be a P.R. guy without being subject to a subpoena in a criminal or civil court proceeding.
The reality here is that Lanny Davis is as much a P.R. guy for himself and his PAYING clients (the Clintons) as he is for Cohen.