The former Newcastle keeper produced a fine display to help the Bhoys to a 2-0 away win over Helsingborgs to put them on the brink of the Champions League group stage.
And his manager thinks that performance would have helped him as it was broadcast on English television and hopes manager Roy Hodgson notices his ability.
"I don’t think he did himself any harm on Tuesday night as far as England recognition is concerned,” Lennon told reporters
"The game was shown to a nationwide ITV audience, so his performance was seen down south. The way he has been the last 18 months, at the top of his game, he’s only getting better.
"It’s not for me to pick him for England but all he can do is keep performing like that and, sooner or later, the door will swing open."
Forster penned a permanent deal at Celtic Park this summer after spending two seasons on loan and Lennon admitted that a lack of international recognition could have made the keeper turn down a full-time switch to the SPL.
|18/1||England are 18/1 to win World Cup 2014 with Paddy Power|
He continued: "There was always that worry that he might not come to us on a permanent deal because when John Ruddy pulled out of the England squad for the Euros, Fraser didn’t even get a call.
"Talks were on-going at that time but the fact we persuaded him to come says that he’s pretty happy at Celtic and feeling good about himself at the minute.
"We’ve had him for over two years now and have bedded him down for another three at least. We feel he is a great signing for us.
"All good goalkeepers win matches for you. Allan McGregor did it for Rangers over the years, Andy Goram did it before that. Artur Boruc did it for us. Peter Schmeichel and Gigi Buffon also did it. Good goalkeepers are worth their weight in gold at times."