The Hoops goalkeeper has not conceded a goal in 1,215 minutes of football, setting a new Scottish record, and is just 96 minutes short of van der Sar's UK best of 1,311 achieved with Manchester United in 2008/09.
Ahead of Tuesday night's Scottish Premiership trip to Aberdeen, Bhoys boss Lennon is hoping the former Newcastle United man can break van der Sar's record as the reigning Scottish champions look to push 27 points clear of the second-placed Dons.
"Fraser was very proud after the match at Tynecastle but he wants to maintain his form. He's got the British record to go for now," said Lennon.
"But it's difficult to talk about breaking records. Our focus is on winning the next game. Both the clean-sheet and undefeated record could go at any time, so we will have to be at the top of our game."
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