Right, I think this is hard to prove. Given that Lombardi was in the NFL for so long, I imagine he's not just making this up -- he probably heard it from players/coaches/execs, so whether it's true or not I think it's interesting he said it.
The game this made me think of was Pats @ Jaguars in September 2018 (Jags won 31-20, their revenge for the '17 AFCCG game), which had a heat index of 107 (apparently one of the hottest games this century, at least since '03:
https://www.espn.com/nfl/recap/_/gameId/401030733). I think it's hard to conclusively say that the Patriots lost because of the heat (both teams had to play in it, obviously) I just remember watching and being truly grateful I was not playing in that game or sitting in that stadium. It looked miserable.