Stoke City were relegated from the Premier League on Saturday as they lost at home to Crystal Palace, but it was expected that Lambert would stay on next season, when his Championship experience will be vital.
Lambert will hold talks with the club's hierarchy later this month but the clause means that the club could sack him without the need to pay a severance fee.
Lambert has publicly insisted that he is happy to remain as Stoke boss. Speaking after Saturday's defeat, the Scot appeared to suggest that he is the right man to lead the team as they aim for an immediate return to the top flight.
“I know what it’s like. I know the amount of games, I know everything about the Championship," said Lambert, who has managed Norwich, Blackburn and Wolves in the second tier.
Stoke chairman Peter Coates has previously admitted that he was happy with Lambert's work since taking over from Mark Hughes in early 2018, but whether or not his position will change now the Potters' relegation has been confirmed remains to be seen.
Relegation brings an end to Stoke's 10-year stay in the Premier League, a record bested by only seven other teams in the league.
Lambert helped Norwich City to earn two successive promotions in 2010 and 2011, and guided them to Premier League survival before leaving to take over at Aston Villa. He was sacked at Villa Park after two and a half years in charge, but re-established his credentials at Ewood Park and Molineux.
Lambert left Blackburn in a similar fashion to his possible Stoke departure, activating an exit clause in his contract.