But at the same time, the manager explained he would make no presumptions about continuing in his current job for some time to come, insisting that football was too fickle a sport for anyone to believe in guarantees.
Desmond was speaking before Celtic's 3-0 victory over Motherwell in the Scottish Cup final on Saturday, a result which gave Lennon his first trophy as manager of the club. The resounding win can only have strengthened the Irish businessman's belief that Lennon, who has been working on a six-month rolling contract, is the right man to guide the club into next season and beyond.
"He's got a very positive and good future," Desmond said. "There's no doubt about it, he'll get a new contract - for a very long time."
Lennon, who had been unaware of those remarks, said that Desmond had offered invaluable advice at times in what has been a very fraught first full season in management for him. "I'm very happy about that and very pleased," he said.
"He's a great supporter of the club. I think sometimes that gets lost. He's on the phone to me quite regularly, and wherever he is in the world he's updated all the time on the team.
"He's been a great source of encouragement and advice. He sees things a little bit differently, as these people do, because they've been hugely successful in their own right in business or in whatever walk of life he's achieved things in. He's a leader in business and he passes down little nuggets here and there that make me think a little bit differently about things. I'm pleased that we could deliver a trophy for the contribution he makes to the club as well."
However, when asked if he would ideally like to see a new contract as the start of a long-term project for himself and Celtic, Lennon explained he could not afford to think in those terms. "I don't do long-term. I'm hoping to be manager next year, and I'm hoping to sit down with maybe Peter (Lawwell, Celtic chief executive] and Dermot, and maybe the chairman (John Reid] as well, and see what they want to offer. They'll hopefully hear what I want to say, and hopefully we can reach agreement on it.
"I don't really think long-term in football, because there's no guarantees. We've made really good progression this year, and I think maybe we'll come back better next year. There's no guarantee that we will, you know, so there's no point in me saying this without being able to back it up.
"I hope the players grow in confidence. I don't think they've done a lot wrong this season in terms of the way they've consistently been playing. So we just need to come back a little bit better, and I don't think we'll be far away."
At the end of Saturday's match, Celtic captain Scott Brown looked like he was trying to convince Lennon to go up the Hampden steps to collect the trophy with him, but the manager refused because, as he explained later, he thought the win should be about the players rather than him. For much of the season, however, Lennon has been the central figure not only at Celtic Park but in Scottish football: the target for letter bombs, threats and an attack.
After the final league match of the season eight days ago, he told the packed stands at Parkhead that he and the club had nothing to reproach themselves for, then at the press conference which followed said he found it "astonishing" that some people said he brought his troubles upon himself. Understandably, Lennon and the club will maintain that stance in the coming months. Nonetheless, the manager did indicate that, while the situation was in no way of their own making, he and Celtic might alter the way in which they tried to deal with it.
"Maybe looking at my own persona," he said when asked what he had thought about changing for next season. "But you're damned if you do and damned if you don't. I don't really want to change too much. There might be a few things. We might adapt our approach to games, to the media even. But not too many changes."
The statement in Lennon's name last week calling for Celtic supporters to desist from offensive chanting is probably the first sign of how the club and the manager want to alter the presentation of him. He has been viewed as a combative figure, even by many with no specific dislike of Celtic, yet here he was offering a more conciliatory approach than those detractors would have thought possible.
It may take some time for Lennon to be seen as a statesman, but, perhaps contrary to the general perception, he is an intelligent and good-humoured man who is capable of learning quickly. Having coped this season with more pressure than most managers have to confront in their entire careers, he has emerged stronger for the experience.
He believes his squad have done the same, and his primary aim now is to continue that process. If possible, as he has already informed Celtic's board of directors, that means making several important additions to the squad over the summer.
"We've already discussed that. They know the areas where we want to strengthen, and we've identified some of the players we think we'd like to bring in, but whether we can do that is another thing.
"I wouldn't think we'd need the influx of players we brought in last year. We'll trim the squad a little bit and hopefully add three or four. Hopefully they'll be quality players, but there's no guarantee of that either. It may be difficult to bring in players who have made the impact of [Beram] Kayal, [Emilio] Izaguirre, [Joe] Ledley, [Gary] Hooper, but we'll do our best."
Besides planning to strengthen his squad, Lennon also aims to improve the contracts of some of the players who, like that quartet, have been brought to Celtic by him. And, just as importantly, he hopes to secure the services of a full-time, first-choice goalkeeper, with Fraser Forster, who has been on loan from Newcastle, his preferred option.
"As a manager you like to give players what they deserve, and certainly some of those players deserve new deals. I think it's important to get a permanent No 1, so that's what we'll look to do.
"We've not spoken to Newcastle yet. [Newcastle manager] Alan Pardew was quoted today saying he's looking forward to seeing him back, but we'll discuss things with them. He [Forster] is a target of ours.
"He's been tremendous, and he's grown as the season went on."
Asked if he thought that he, like the players he mentioned, was entitled to a bigger and better contract than he has at present, Lennon again stressed that he was taking nothing for granted. "No, I didn't say that," he stated. "I didn't say that. Again, we'll sit down and negotiate. Whether I get an improved contract or not remains to be seen."
It does, but surely not for much longer. Originally employed as no more than a stand-in when he took over from Tony Mowbray last year, Lennon is now about to be acknowledged as a sitting tenant, with - whether he wants to think in those terms or not - the long-term rights which go with such a status.