Forster has been drafted into the squad for the World Cup double-header against Montenegro and Poland but coach Roy Hodgson has already stated Joe Hart will remain his No 1 choice.
Hart's position had come under scrutiny after he was blamed for two of Bayern Munich's goals in their 3-1 win at Manchester City on Wednesday.
The previous night Forster had fired a timely reminder of his capabilities when putting on a stunning display to limit Barcelona to a single goal in their Group H tie at Parkhead.
Speaking on Sky Sports News, Lennon said: "It's a shame it has to take Champions League performances for everyone to sit up and take notice as he's played like that for a while.
"It's brilliant for him and testament to his talents. He is playing his club football in Scotland yet he is knocking on the door for the England spot.
"There is no question that he has to stay focused now and has to understand that Joe is No 1 ahead of the two crucial World Cup qualifiers and also understand Roy's take on it.
"But he has rubber-stamped his credentials to the point the England manager is talking about him when referring to upcoming games.
"It is his talent that has got him there. People laughed at me a couple of years ago when I was saying how good he was but he's justifying what myself, Stevie Woods (goalkeeping coach) and the backroom team think of him."
Barcelona defender Dani Alves is also a big admirer of the former Newcastle keeper and believes he would be the ideal man to replace Victor Valdes who is leaving the Nou Camp next summer after 11 years with the club.
Alves, part of Barcelona's victorious side on Tuesday, said: "We have played Celtic three times in the last year and each time Fraser Forster has been fantastic.
"Barcelona are a club who are always looking to add quality and Forster has real quality. If it ever happens, he would be a good addition to our club."