The former Magpies hero believes the Spanish manager should walk away in the summer if they go down.
The Magpies have endured a terrible season, in or around the relegation zone for almost the entirety of the campaign, but there have been signs of life in the last week under the Spanish boss.
The North East club got their first win under the former Liverpool and Real Madrid head coach on Saturday with a 3-0 victory over Swansea City, and they followed that up with a spirited 1-1 draw against Champions League semi-finalists Manchester City on Tuesday night.
However, the club are still in grave danger of relegation despite the improvement, and sit two points off Norwich City and safety with just four matches of the season remaining.
Lee, who played 379 times in a decade for Newcastle, is of the opinion that Benitez will not look to stay on at the club if he does not manage to keep them up as he would be a bad fit in the Championship.
The 50-year-old told 888sport: "If they go down he is definitely not staying, there is no doubt about that. And it’s right that he doesn’t because with all due respect he doesn’t know that division.
"He’s got a great track record as a manager but he’s never been at a club that is in such dire straits as Newcastle. At Liverpool and Real Madrid they had very good players. Newcastle at the moment haven’t."
The Magpies have four games to saves themselves from doom, starting with a trip to Jurgen Klopp's in-form Liverpool this weekend.