IF Celtic had produced a job advert in order to replace Brendan Rodgers after he left to take over Leicester City, the checklist for their ideal candidate may as well have described Neil Lennon right down to his ginger hair.

Someone to come in, preferably with an in-depth knowledge of the club and how it operates, to keep a well-oiled machine ticking over as it steams towards a third-successive treble. Simple, right?

As much as Lennon fitted the needs of Celtic to a tee at the time, and however well he has handled those demands since he temporarily – for now, at least – took over the reins, he was at pains to stress after a fraught Old Firm tussle at the weekend that the assignment has been far from straightforward.

Whether the mutually beneficial arrangement will continue beyond this season remains to be seen. The victory over Rangers on Sunday will strengthen Lennon’s hand to return permanently to Celtic Park, but it will likely only be the deliverance of the Scottish Cup along with the Premiership title that will see him gain a vice-like grip on the position.

And he is at pains to point out that if such success is delivered, due credit should come his way for the part he has played.

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Lennon said: “I think from the outside looking in, people look at it and think: ‘That’s an easy job, you are just picking up the reins from where Brendan left off’, but there are adjustments that you have to make to the staff, the training structure, the players and the mentality of the players.

“I didn’t make this situation. I have come in and answered the call and we are doing alright.

“I would hope people would think the club is in a safe pair of hands. We have won four out of five. We have got over a big psychological hurdle on Sunday and we are now 13 points ahead in the league.

“Since I have come in, we have extended our lead by five points and we are in the semi-final. We haven’t done a lot wrong.”

Based on results alone, that much is inarguable, but there was enough to concern Lennon in the performance against Rangers to convince him that a major overhaul to this team is needed in the summer.

He hopes he will be the man to carry out the rebuild, but in the meantime, he will continue to tweak and tuck at the successful formula laid down by Rodgers to iron out the foibles in their game and ensure that they don’t trip up so close to the season’s finishing line.

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“[The Rangers game] was fraught,” he said. “It shouldn’t have been as fraught as we made it because at half-time we were a goal up and had a man extra. There was a little bit of naivety from us at times in the game.

“I thought we were a little bit passive in the second-half in terms of our pressing. We sat off Rangers and [Ryan] Kent and [Daniel] Candeias kept coming off and getting turned. We really should have been 10 yards further up the pitch to stop the attacks around about the halfway line.

“I am not going to reinvent the wheel. It’s simplicity. Just the little nuts and bolts of the game that we can do better.

“When we were down to 10 men, we were too passive and too deep. Allan McGregor makes a good save from Scott Sinclair. If it had gone 2-0 then we would have been in control of the game.

“Then they equalise and there is an anxiety around the ground and the psychology of the game changes. Then Rangers are on the front foot even though they are down to 10 men.”

Flaws in Celtic’s psychological make-up have been few and far between in this period of unprecedented success across all domestic competitions, but Lennon has noticed a propensity to think that the job is done before it actually is, although his team have so far shown the mental resolve to recover any situations they have temporarily allowed to slip.

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“We did it at Hearts as well,” he said. “We went a goal up, they went down to 10 men and we conceded a goal early in the second-half that made it difficult for us. We did the same again.”

Such concerns are exacerbated in the longer term by an acknowledgement of an improving challenge from across the city.

“To be fair to Rangers, they played well,” he said. “You have to give them credit. It was a cracking game of football. I thought for an hour we were superb, but you always need that second goal to put the psychology of the game well in your favour. At 1-0 anything can happen – and it did.

“Have Rangers improved? Yes. When they came to Hibs at Easter Road in December, I thought they played really well and then we played them at Ibrox and we got a good point there.

“I mean, they had to improve on last year because they were all over the place a little bit. Steven has gone in and added a bit of steel.

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“On our first hour showing, we are well ahead. To be fair, it might have the last throw of the dice for Rangers on Sunday and they threw everything at it, but we overcome that.

“They have good energy and have some good players there, but we just have that little bit better at the minute and long may that continue.”

As Lennon hopes to be witnessing the dawn of a new era under his leadership at Celtic, the sun looks to have set on Dedryck Boyata’s time in the green and white hoops.

The Belgian international defender looks a certainty to leave the club in the summer, and having hobbled from the action on Sunday clutching his hamstring, it may be the last that Celtic supporters see of the 28-year-old.

“Possibly,” admitted Lennon. “He felt it [hamstring] rip. He played on having felt a twinge and then he felt a rip five minutes later.

“Again, we’ll have to wait and see, but it’s a blow because he’s been absolutely brilliant.”