Incoming Celtic chief executive Dominic McKay will not be allowed to make his move to Parkhead early as Murrayfield bosses insist he sees out his notice period.
McKay will be expected to lead the hunt for Lennon's successor when he takes over, while a behind-the-scenes restructure means the recruitment of someone to fill a director of football role will also be high on the Scottish Rugby Union director's to-do list.
However, Murrayfield chief executive Mark Dodson is adamant McKay – who currently serves as his number two – will be going nowhere until they find a new man for his position as the SRU's chief operating officer.
"What's happening at Celtic is out of my control," Dodson said. "It's not something I'm utterly familiar with but I do know Dom is going to have a very full in-tray when he gets there.
"The issue for us is that he has a notice period that he has to serve here and we need stability in our business too.
"So I expect Dom to be here with us for a while.
"We're going though a restructure process of our own here anyway so Dom moving to Celtic just gives us a chance once more to look at what we're going to do.
"But yeah the roles will be replaced and we'll make sure that we take our time and get some outstanding candidates to replace Dom."
Lawwell has faced furious supporters protests on the doorsteps to Parkhead this year as Lennon's team lurched from one crisis to another.
The febrile world of football is a million miles away from the more sedate rugby surroundings McKay is used to, but Dodson has backed his colleague to make a successful transition.
He said: "Dom has been here for a decent amount of time and he's been instrumental in the transformation of Scottish Rugby in a commercial and sporting perspective.
"He's a really talented guy and personally I'm close to him and know what a good operator he is.
"There are different pressures in rugby than in football but he's a smart individual, he's a very experienced operator and I'm sure he will adapt."