The midfielder moved to the Toffees on loan from Manchester United during the deadline day.
After coming off the bench in Tuesday’s 3-1 loss at Newcastle, van de Beek was given an outing from the outset against Leeds at Goodison Park.
And the Dutchman delivered a fine display in the engine room to inspire the Blues to victory.
Van de Beek did go down with a problem in the 55th minute, however, and received medical treatment.
But Lampard insisted that van de Beek was fine and his problem was likely due to a tough 90 minutes against a high-octane Leeds side.
Lampard said: “I think so [everything was OK]. He didn’t say anything to me.
“I just spoke generally to the lads and I think something would have been flagged.
“I just think the 90 minutes told on him. He hasn’t played a lot of 90 minutes, it was a really difficult 90 minutes physically for everyone today but I think he’s OK.”
On van de Beek’s performance, Lampard said: “I know Donny a player from the outside and brought him here because of his talent.
“He can play, he’s intelligent, a real technical player.
“He was part of a really work ethic type of performance. He matched the other players, was calm, linked the play, confident on the ball and that’s exactly what I brought him here to do.”