Lennon spent time with Moyes and Sir Alex Ferguson in Manchester on Thursday evening at a dinner to raise awareness and funds for ulcerative colitis, the bowel condition which affects Darren Fletcher. More than £100,000 was raised at the event and inevitably football dominated the dinner table discussions.
While Lennon's stock is high at Celtic - they will celebrate winning a third consecutive league title after today's home game against Ross County - he has had moments of friction with the Celtic support and found it easy to show his empathy for the beleaguered United manager.
Moyes, a former Celtic player, is the target of a cheap stunt this afternoon at which a light aircraft is expected to fly over Old Trafford during the lunchtime game against Aston Villa. The plane will trail a banner saying: "The Wrong One: Moyes Out". The wording is a play on the "The Chosen One" banner which hangs at Old Trafford's Stretford End, alluding to the anointment of Moyes by Ferguson last summer.
"What I'm not happy about just now is the way people are rounding on him at the minute," said Lennon.
"You don't mind constructive criticism but when it comes to the point they're trying to humiliate him it leaves a sour taste in the mouth. He deserves a lot more than that and should be treated with more respect. Any manager can have a bad run of games but I certainly don't think he should be treated that way.
"It's a transitional period for Manchester United, difficult times, but one I don't think will last that long. I think he'll be given time, and rightly so, and I think he'll get it right. I have a little understanding of what David is going through but I can't second guess how he's feeling.
"Like all managers' jobs when you go through a rough period, it's a lonely place to be. He's a strong enough personality to overcome it and he's got a lot of support. A lot of people in football want him to do well, myself included.
"David has had a bit of money and it's up to him how he spends it. We're human beings and as long as you don't get over-sensitive you accept criticism as part of the job. You can't have it your own way all the time. There are bits and pieces which, while you don't want to hear it, you have to put up with sometimes."
Lennon was jeered by some Celtic supporters for his perceived negative play during a UEFA Cup tie against Boavista in 2003. As manager he has faced periodic criticism after poor results, notably losing to Ross County in the 2010 Scottish Cup semi-final, some early disappointments in European ties and a famous league game at Kilmarnock in 2011 - before he had won any of his titles - in which Celtic trailed 3-0 at half-time before recovering to salvage a point.
"I can identify with it," he said of the treatment Moyes has received. "The Kilmarnock day, when we were 15 points behind and 3-0 down at half-time, I was walking down the tunnel thinking: 'Ciao! Sayonara! I'll get my coat!' All those things go through your head.
"We were fortunate enough to turn things around and I'm pretty sure David will as well. He's got a big job on, rebuilding the team. But it's the tacky criticism such as the plane that annoys me and it's disappointing when it even gets air time. We should ignore it."
Ludicrously some supporters verbally abused Ferguson after United lost 3-0 to City on Tuesday evening. "What do they want? Are they real fans or did they just jump on the bandwagon on the back of Fergie's success for the last 15, 20 years? I have no idea how he can be getting pelters. It makes you ask yourself why you do it.
"But in Sir Alex's case it's water off a duck's back. He might be a little bit upset about it and if he is I would understand it but I don't think he can take any blame for it.
"Sir Alex is as disappointed as David but when we spoke the other night we didn't dwell only on Manchester United. He actually said he had a bet on us on Wednesday night and it actually came in.
"That was pleasing because when he backs us we usually get beat. He was in great form."
Celtic have been too, of course. They have not conceded a league goal at Parkhead since November. A pitch invasion aborted a planned celebration when the league was officially won on Wednesday night but there will be a lap of honour after today's game against County.
Celtic have nothing especially significant to play for but they could still reach 105 points by winning all of their seven remaining games. The record is 103, set by Martin O'Neill's team including Lennon, in 2002.
"The records are academic, it's about the team and the style of football I want to play. But it would be the ideal way to end a good league season. Ideally I would like to break the 100 points. Whether we get to that 105 points mark is another thing but it would be nice.
"Another goal we are aiming for is our defensive record. We have only conceded 15 goals this season and that is absolutely brilliant. I think the record for goals conceded is 17 or 18 and we are looking to break that too.
"We want to win the game against Ross County and party. We want to perform and entertain and the shackles are off. We've also a duty to Kilmarnock, Partick Thistle and St Mirren to make sure we compete."
Charlie Mulgrew and Adam Matthews are doubts today. Lennon is resigned to losing Georgios Samaras, whose contract is running down, in the summer but he will not freeze him out of the side.
"I will give him some games now so he can go to the World Cup and be in decent condition for Greece. If he does leave this club he has been a very good player for me and he can leave with his head held high."