The Celtic boss will be delighted if his giant shot-stopper is given the chance to prove himself ready to push the Manchester City for the England No.1 spot by winning his first cap against Sweden next week.
The £2million Celtic paid Newcastle for 24-year-old Forster is already looking like a steal, comparable to the £900,000 paid for another rising star, Victor Wanyama.
The pair were outstanding in the victory over Barcelona in midweek, and interest in them from top clubs down south is already growing.
Lennon said: "The goalkeeper had two amazing performances against Barcelona on the back of some other great performances.
"I expect him to keep his place in the England squad and I think now he is pushing Joe Hart.
"He's playing at the highest level and playing brilliantly.
"That, to me, is an indication he could play for England, and I want him to push Joe Hart.
"I'm not saying Fraser is the best in the world. It's all about opinions, and I think he has the potential to be anything he wants to be.
"He works really hard – he was in yesterday – and is a very grounded individual."
Goal hero Wanyama is similarly reaping the benefits of being given the coaching and opportunity to develop at Celtic, and Lennon made no attempt to hide his admiration for the Kenyan.
"Victor did not look out of place on that pitch," said the manager of his Barca performance.
"He showed another aspect of his game with a burst of pace we had not really seen before.
"We all know he is technically gifted and a powerhouse, but there was more to his game on Wednesday."
Lennon hopes both will stick around to develop even further in his team, and is also resistant to any suggestion he himself might be a man in demand for his achievements.
"I don't envisage getting an occasion like Wednesday anywhere else," said Lennon.
"This job is great at the minute. A year ago, it was not so great. In a year's time, you don't know what it will be, if I'm here or not. You just take it as it comes."
Lennon's next task is to rediscover the winning thread in the SPL, but he will have to go into tomorrow's game against St Johnstone still without Gary Hooper, who it is hoped will be back for the tie against Benfica a week on Tuesday.
Scott Brown is also expected to miss the SPL match due to a virus.