"It's not connected at all," said the Hoops boss.
"It's Johan's decision. It's been in the pipeline for quite a while. We talked about it months ago."
Lennon has begun to headhunt the man to replace the Swede, and revealed news of Mjallby's departure has prompted a flood of applications.
Three men already widely tipped are already ruled out for the No.2 spot.
Of current first-team coach, Garry Parker, Lennon said: "I'm looking for a No 2, so I won't promote Garry."
Of development squad coach John Kennedy, he said: "It's too early for John just yet, and he is quite happy doing what he's doing."
And of former team-mate and club icon Henrik Larsson, Lennon said: "No, Henrik's just got a job in Sweden, and I'm not too sure he'd want to come in as a No.2.
"I think he likes doing his own thing and I'd probably be looking for someone with a bit more experience than that."
Even though Parker and Kennedy are not in the frame, Lennon has not discounted promoting from within the club, saying: "That's an option, certainly. But the phone has been red hot already this week.
"I will sit down with Peter Lawwell within the next couple of weeks and go through some candidates.
"There is no rush, but it is an important decision I'd like to get right."
Lennon wants the new man to be in situ by the time the squad return from their summer break on June 24.
He hopes to attend the opening stages of the World Cup Finals in Brazil, so it would be preferable if his assistant is appointed before he heads out there.
Lennon admits he tried to talk Mjallby into staying, but respects his former team-mate's reasons for moving on.
"He's got his own ambitions and interests he wants to pursue," said the Hoops boss.
"I tried to talk him out of it on a few occasions. But you know Johan, he's very strong-minded.
"He thought four years was enough. He's been away from his family for over 18 months, and that can take its toll as well.
"So I fully understand it. I'm very disappointed, obviously, because he's been with me since day one.
"He was my confidante, and someone whose opinion I really trusted and still do.
"Even if I do bring in someone from the outside, there's got to be a feeling from myself I can go to this guy, I can pick his brains, or I can trust his opinion.
"Now whether I agree with it - and I didn't always agree with Johan - is another matter.
"Ultimately, the decision is mine when it comes to football and ultimately the decision will be mine on who I bring in."
Mjallby - who has business interests in his homeland - is already on the radar of his previous club, AIK Stockholm.
AND, although Lennon would like to work with him again in the future, he believes Mjallby could become a boss in his own right.
He added: "He's certainly got the personality for it and the experience of the four years he has had here to stand him in good stead wherever he goes."
Lennon wants to find another assistant will all of the qualities that Mjallby brought to the job.
But the prospect of introducing someone with new ideas clearly excites him.
Lennon said of the applicants already in touch: "I've been impressed.
"CVs have come in as well, and it's something to pore over.
"Ideally, if the guy is astute on the training ground, he might bring something fresh to what we are doing here - maybe European experience as well.
"That's not a necessity, but it would certainly help. It doesn't have to be someone I know, but it might be.
"It's important the person we bring in will have a rapport with the players as well. So we'll have to gauge his personality, too."
While he makes plan for his fifth season in the job, Lennon took time to consider how Ryan Giggs must be feeling as he prepares to be interim manager of Manchester United for the first time today.
It brought back memories of when he was pitched into a similar situation four years ago, and Lennon said of the parallels: "If there is an opportunity there for Ryan to take it, he should grab it with both hands and try and make the most of it.
"He's got nothing to lose. If anyone deserves a crack at it, it would be Ryan Giggs, for the service he has given to Man United over the years."
HOWEVER, Lennon is bitterly disappointed Giggs' opportunity is the result of David Moyes' sacking.
He said: "What appalled me was the way David was treated, certainly over the last three or four months, to the point where people were trying to humiliate the man.
"So, yes, I'm surprised they sacked him.
"Being Man United, you just felt, with the way they had been run for the last 15 years, they would have given him a bit more time and been a bit more understanding, in the circumstances.
"It's indicative of the way the game is going. It's certainly a worry for all managers when you see that sort of thing happening.
"It's almost as if the 11 years he had at Everton have been wiped out. People have forgotten about them.
"What disappointed me last week was the reaction he got from the Everton fans. It was really disappointing, considering the sweat that he put into that club.
"Eleven years is a lifetime. They are reaping the rewards. Roberto Martinez has come in, but the platform was already in place and was put there by David."