The pair enjoyed huge success together as player and manager, winning the Premier League back-to-back in 2005 and 2006.
Lampard has since become a manager and is now in charge of Chelsea, a direct rival to the club now managed by Mourinho, Spurs.
Although the pair have often spoken of their admiration for each other on a personal and professional basis, there have been moments on the touchline when they haven't seen eye-to-eye.
“I have been at a couple of the games between them and I have watched them closely - there's a bit of needle on the touchline which is good to see,” Robinson told the Racing Post.
“Frank likes to show he is no longer the pupil and stands up to Jose to prove to him he is no longer the pupil, which I am not sure Mourinho likes.”
After being sacked as manager of Man Utd, Mourinho took a short sabbatical from football before eventually being hired to replace Mauricio Pochettino at Spurs.
Although his status as one of the very best coaches in the world may be on the decline following the stint at Old Trafford, Spurs decided his reputation was enough to bring him in.
Robinson believes he can lead Spurs to trophies.
“Jose was brought in for one reason - to win trophies - and I genuinely believe he can do that with the team he has," he added.
“He knows he can be part of history if he can win with Tottenham and you saw that in the week when they played Chelsea in the Carabao Cup and had Europa League qualification two days later. He picked teams to win both games. Jose is looking to keep his balls in the air for all competitions.”