Southgate, who can sympathise with Lambert's plight, was sacked when Middlesbrough were fourth, one point off the Championship leadership.
He is adamant that must not happen to Lambert.
"It was a big gamble by Lambert and Villa because I did it myself and the difficulty is that young players will make mistakes. You have to live with that," said Southgate. "There is an element of risk. When it gets to the end of the season you are never sure how they will react, but the last few weeks have been good for Villa.
"Even if Villa go down, I don't see why you would change when you have a guy there as manager who has had success before. That would be a mistake.
"Villa should not change having put this policy in place. They should stick with it."