Neilson struggled to win over the entire fanbase in Gorgie during his two and a half years in charge, despite leading the team to a record-breaking Championship title triumph in 2015 before masterminding a third-place finish in the top flight last term.
Some supporters even cite last season’s Scottish Cup replay defeat by Hibs, after throwing away a two-goal lead in the first game, as a reason for not being enamoured with Neilson – who is set to take over at Sky Bet English League One club MK Dons – after their bitter city rivals went on to end their 114-year heartache in the competition.
But former Celtic manager Lennon, who has yet to sample an Edinburgh derby having been appointed Alan Stubbs’ successor last summer, has been impressed by Neilson’s maiden managerial stint.
“Robbie has done a very good job at Hearts. What more could he do?” asked Lennon.
”The Scottish cup loss to Hibs last season was just one game and you have to look at the two and a half years that went before.
“He got them promoted from the Championship, they finished third last season and they are second in the Premiership right now.
“That is pretty impressive. Sometimes you have to be careful what you wish for.
“Hearts have been very impressive under Robbie in the last two and a half years and why that has divided opinion, I don’t know.”
Lennon appreciates how demanding English football can be, having spent 17 months at financially-stricken Bolton Wanderers before departing the club in March. The Northern Irishman, however, also understands the appeal in leaving Hearts for a team who are 19th in League One.
He added: “There are pros and cons. Firstly, if you look at the last manager, Karl Robinson, who I know very well, he was there for six years, which is a lifetime in the modern game. So you’d like to think he’s going into a stable environment.
“They get good crowds as well, but the flip side of that is he sees Hearts playing well against Rangers in front of 17,000 people, so then you’ve got to consider ‘why would you give that up?’
“The only person who can answer that would be Robbie, depending on his own personal ambitions.
“Maybe he wants a crack at England and sees this as his opportunity to progress his career.
“He’s still young but ultimately the difference between Scotland and England is money.
“People ask why MK Dons can attract a manager going very well at the top of the league in Scotland.
“It’s because, even in League One, they can pay a lot more money than Scottish clubs. I’m not saying that’s the sole reason he’s going but it’s an incentive.
“What he will have to get used to is the brutality of it all.
“It is relentless, it’s a 46-game season and you are playing Saturday and Tuesday every week.
“He will have to manage his squad as best he can and use the market as best he can in January.”