The Blues went top of Group H thanks to substitute Michy Batshuayi's late goal.
Fellow substitute Christian Pulisic showed supreme skill to find space down the wing and deliver a cross to Batshuayi, who rectified an earlier miss by converting from close range.
Ajax did have a goal ruled out by VAR, but it was the visitors who dominated proceedings and deservedly set up a tantalising clash between the two top sides at Stamford Bridge.
Speaking after the game, Lampard said: "You try and give players information, you don't want to overload them, but you've got to give them information against a team like Ajax.
"Our end product has got to be better on nights like tonight, the scoreline could have been more. These young players want to take on information and the older players are great examples, look at Jorginho tonight, he was phenomenal.
"We haven't had many VAR breaks this season so maybe we were due one. For the great team that they are they didn't have Kepa under too much pressure."