Lampard has been in interim charge at Stamford Bridge for the last nine games, losing seven, and his short-term contract will expire at the end of the season.
He is expected to focus on trying to get another managerial post after previous spells in charge of Derby, Chelsea and Everton while Pochettino is likely to be joined by his usual backroom staff of Jesus Perez, Miguel D’Agostino, Toni Jimenez and his son Sebastiano.
And Lampard said: “A new manager will come in and bring his own coaches, for sure.”
Chelsea gave new champions Manchester City a guard of honour before Pep Guardiola’s side beat them 1-0 at the Etihad Stadium and Lampard urged his players to show the same work ethic if they want to emulate them.
He added: “I don’t think they should have to do a guard of honour to understand. Manchester City have not won three [Premier League titles] in a row through half intensity. They have had to work and work and work. The players have to understand that. They have to take personal responsibility and say: ‘I want to be [Erling] Haaland or [Kevin] De Bruyne, I have to put in the work they have.’ It is something they have to strive towards.”
Chelsea will finish in the bottom half of the Premier League this season but Lampard believes it is up to the players what they achieve in the future.
He said: “It is in their hands. I can’t say that how long it will take. It is down to the players and the direction of the club. This Premier League is getting tougher.”