England goalkeeper Forster will beat former Aberdeen goalkeeper Bobby Clark's 43-year-old record if he keeps Hearts out for 31 minutes of their Premiership meeting at Tynecastle on Saturday.
The 25-year-old has kept 12 consecutive clean sheets in the league but former England goalkeeper Peter Shilton has been among those to detract from his feats in recent weeks by claiming he is not tested enough in the Scottish game.
Lennon said: "I think Celtic has been good for him, given him a platform where he has progressed to the England squad.
"Regardless of what people think of the Scottish game, he has to make plenty of saves going along.
"It's not just his Champions League form that's propelled him into the public arena down the road.
"He has got better every year, he has won trophies here, he is on the verge of breaking a clean-sheet record.
"It's not as if he is standing idle for 90 minutes and has to produce a save or two. He has had to make some big saves along the way.
"His performances last year in the Champions League were a primary reason why we got to the last 16, and he has kept his focus, his determination and dedication to the position going, to the point where we are talking about breaking clean-sheet records.
"He has got plenty of motivation, he has hopefully the World Cup to look forward to. He must maintain his high standards to make sure he travels to Brazil."
Lennon stressed the potential record was not just down to Forster and admitted his surprise that centre-back Virgil van Dijk had not made Holland's provisional World Cup squad.
"I'm surprised because I think he is good enough to get in a provisional squad of 33, but it's something that he can't dwell on," Lennon said.
"He has played very consistently domestically and he was superb in the Champions League.
"He is only 22 so he has a lot of scope to get even better. But he is what you want in the modern-day centre-half: he is big, has great timing in the air, technically proficient with both feet, has good pace and can read the game very well.
"We knew we had a good player, but it's his temperament that we like as well. He has a fantastic attitude to the game."
Meanwhile, Lennon played down suggestions that the club had forced Joe Ledley into a January departure by accepting a bid from Crystal Palace on the final day of the transfer window.
The Wales midfielder this week claimed he was going to sign a new contract before the decision from Celtic led him to move to London.
But Lennon said: "The contract was on the table for quite a period of time. It's not as if it was a last-minute thing. It was on the table for at least two or three months.
"There was a big part of him wanted to stay, but a big part of him wanted to play in the Premier League as well.
"Unfortunately, we lost out and lost a very good player."
Meanwhile, Celtic will travel to Kilmarnock on Friday, March 14, after the match was brought forward from the Saturday for live TV coverage on BT Sport. The game kicks off at 7.45pm.