He told BBC Radio Cambridgeshire: "There's always a good chance when a new manager comes in that it might not be the club for you any more.
"What the gaffer thinks of you when he first sees you is massive."
With Posh already relegated from the Championship the players have only two more games to convince Johnson, the club's fourth manager of the season, that he should keep them on for next season.
Saturday's humiliating 6-0 defeat to Reading would not have helped anyone's cause, but Lee is trying to learn from the result.
He said: "Reading did a lot of good things, they put the pressure on from the start and in the next couple of years that's what we've got to get to.
"We're not giving up on this season. We've got a lot to learn from the next two games and then take it into next year."
Peterborough's remaining fixtures see them play Blackpool at home before making the long trip to Plymouth Argyle.
Source: BBC Sport
Source: BBC Sport