Van de Beek became Lampard's first Everton signing after
joining on loan from Manchester United for the rest of the season on Deadline Day.
Frank Lampard on VdBeek.
The Dutchman, who struggled to break into the starting XI at United, was given his first Everton start against Leeds and excelled in central midfield as he helped
the Toffees to a comfortable 3-0 win.
The 24-year-old's eye-catching performance came despite it being his first Premier League start of the season.
"He's a technical player but he matched the other players for work ethic. He gave us a sense of calm and he linked the play.
"He looked confident on the ball and that's exactly what I brought him here to do."
Van de Beek was deployed as a central midfielder alongside Allan in a 4-4-2 formation by Lampard for the win over Leeds.
The Netherlands international made his name as an attacking midfielder at Ajax, having scored 41 goals in all competitions over his final three seasons there before he joined United.
Questioned about his role under Lampard, the Englishman said: "I think he can do different roles and that's the beauty [of him] and why I moved so quickly to try and get him when I came in.
"I'm a big admirer of him as a player and I think he can do both roles for us. He played as one of two midfield players today and I know he's got the talent to link and get us through the lines of the pitch with his passing, and he also has the work ethic needed in that role.
"I think and I know he can do a higher role, and he's a goal threat too, so that's one of the big pulls of me bringing him in, knowing that he can bring different elements of his game to help us in different ways.
"When called upon to do that discipline role today, I thought he did it really well."