But Lennon insists the Irishman is equally passionate about the club.
Celtic shareholders questioned why Desmond did not attend Friday's AGM at Celtic Park, but Lennon revealed he was in regular contact with the billionaire.
Lennon, who received two touchline bans from the Scottish Football Association last season, said: "I speak to him at least once a week. He is as passionate as I am.
"He gives me good advice but has also given me a talking down at times about my behaviour on the touchline or my demeanour.
"I spoke to him (on Thursday) and he was asking about the players coming back from international duty, what condition they were in.
"He is always looking for me to find a different angle, an edge.
"I guarantee he has the best interests of the team at heart."