I'm sure Pats fans will hate Bill Bellichick when he goes after not winning again and being mediocre for last few years.
If they think Belichick's management style is actively harming the team, they will feel differently about him, yes. I don't think they will feel that way and it's a false analogy. In Lou's final season, the Devils were the oldest team in the league, they were capped out, they were being coached by him and two assistants, and they finished 6th worst in the standings in a year when 3 franchises were actively trying to lose.
Lou has a tremendous legacy and they may well build a statue for him outside of the Prudential Center someday. He also left the franchise in a deeper hole than almost any team has been in the last 10 years, partially out of necessity, partially out of neglect. If the Devils can start winning, all of this stuff can hopefully go away, but I know it won't.