The Swede returned to Parkhead last week to become number two to Lennon, who took charge after the shock 4-0 defeat at St Mirren a week past Wednesday brought an end to Tony Mowbray's tenure. Mjallby, who played for the Hoops between 1998 and 2004, had been coaching youngsters in Sweden but he had no hesitation in flying back to Glasgow to help his former team-mate instil passion into the Parkhead dressing room.
Speaking at Lennoxtown, where he was helping to publicise the club's player-of-the-year awards dinner, the former Celtic defender said: "Lenny phoned me because he knows what I am like. I won't change. Neil is very determined, passionate, played the game at the highest level and it has always been easy to motivate those around him.
"I remember when Neil and I were fighting a wee bit on the pitch but as soon as we were back in the dressing room then we were fine. That's the way it should be done.
"There will always be times when you raise your voice and are not happy about things, but as long as the players sort it out, we are fine about it."
Mjallby insists he has slipped easily into his first coaching role.
He said: "I am direct and expect a lot from the players and myself, so I don't think it is going to be a problem. I have been very impressed by them. There is a lot of talent and maybe they are just lacking in confidence.
"It's a difficult situation. We don't have that much time so the main thing is to lift the spirits. The talent is here so hopefully we can get on a winning run.
"Obviously it is a bit different when you are over here at the highest level as opposed to Sweden, where I would probably get a wee bit frustrated because I'm used to being around players who play for big clubs.
"If you start in the lower leagues in Sweden most of the guys are going to be semi-professional if they get any wages at all. Then it is hard to expect a lot from them.
"So I think it is easy to melt in here because I am used to the atmosphere around Celtic and I am used to the expectation."