It was March 2010, Tony Mowbray had just been sacked as Celtic manager and Lennon was taking over on a caretaker basis. Did Mjallby fancy joining him? Realistically it was going to be a short assignment, a two-month job to see the team through to the end of the season. The championship was gone but there was a good chance of winning the Scottish Cup. Mjallby gave it a few seconds' thought then agreed to become Lennon's assistant. He would likely be back home in Sweden by the summer.
Instead he has stayed a bit longer. Four years longer, in fact. A shock semi-final defeat to Ross County ended those Scottish Cup dreams but eight successive victories in the league were enough to earn Lennon the job on a permanent basis. Mjallby elected to stick around too.
As he prepares belatedly to move on after next weekend's final game of the season, he concedes it has been well worth his while as three league titles, two Scottish Cups, three seasons in the Champions League, including a win over Barcelona, will all testify.
"We've been really consistent and played well," said Mjallby as he analysed his tenure. "It's been mostly ups in my time here and we've been quite successful, winning the league and doing well in Europe. We've also brought young players in and improved them, and that's important for the club right now. Some of them have been real success stories, the likes of Victor Wanyama - buying him for not too much money and selling him on for a lot of money which was very good business for the club."
So what now for Mjallby? Surprisingly, he doesn't seem to have anything fixed up despite rumours linking him with the manager's job at AIK Stockholm. He would not rule out popping up somewhere in the role of assistant manager once again, and is not definitely heading back home to Sweden. Instead, he is looking forward to a period of rest and reflection, preferably with the sun on his face.
"Looking into the future, I would probably like to try [being a manager] one day but I'm very happy being an assistant manager as well you know," he added. "It's a position I feel comfortable in as well. So I'm not ruling anything out. I'm still under contract until May 11 so it's not like I've been trying to find my future lately, I'm going to leave that for a wee while anyway and try to get a few weeks holiday. I'll see what happens and see what comes in."
And what of Lennon? Mjallby felt his friend has improved year on year during their time working together. "Neil is definitely a much better manager now," added the Swede. "He is calmer now, although he is still passionate and still has that hunger. Tactically, he has improved a lot.
"He is very interested in all football around the world. He goes to watch a lot of European games and players, he goes to see other managers. I have to say he has improved a lot tactically and I think we would see that last season in the Champions League. It was a great learning curve for all of us. We really had to prepare the team well before those games."
Not even Lennon at his feistiest would surely fancy taking on Mjallby in what would probably be one of the most one-sided square goes of recent times. Thankfully for the Northern Irishman, the pair never came to blows. "He isn't a hard mark to work with - not for me, anyway," said Mjallby. "Maybe for the players. I had the benefit of playing in the same team as him for four years and we used to argue on the pitch most of the time anyway.
"There hasn't been a problem, we have worked really well together. We have never, ever fallen out. Sometimes we might not have the same view on things, but I wouldn't be a good assistant manager if I always had the same view as him. He can bounce things off me, then we sit down together to speak about the team."
Mjallby was also confident that Lennon would not be leaving Celtic in the near future. "Neil is obviously not going to be at Celtic forever but I think he is very happy being Celtic manager. He feels at home here and he knows Celtic inside out. He knows what a big club it is and that hopefully there will always be the chance to get into the Champions League. He loves Glasgow, so does his family. So I don't see him moving on any time soon."