As good as I think Lombardi was as a HC, I don't think he compares to what BB has managed to accomplish. The biggest reason being that the competition and difficulty to win championships is so much more difficult now than what it was back then. The best and simplest example is how many teams you have to go through in order to win a championship. To win a championship in 1958 you only had to beat 11 other teams. Now you have to beat 31. And that doesn't include all the cap and contract limitations. You only had 12 games to play, and at the most 2 playoff games, etc etc etc.
Than being said, I would always keep the championship trophy as the Lombardi. That is the its identity and has been for decades. I'm sure there has been more important and impactful members of the NHL than Lord Stanley, but NO ONE is looking to change the name of the cup to honor, say Gordie Howe, or Bobby Hull, or Bobby Orr, etc
I thank Willie for making the case, but it is NOT about who is the better HC. It's about tradition. It was already the Lombardi Trophy when BB was just a gofer in Baltimore at $25/week (plus room and board) in the early 70's.