Havertz, the £70million summer signing, spearheaded Chelsea's 6-0 hammering of Barnsley with his first goals for the Blues since joining from Bayer Leverkusen earlier this month.
Tammy Abraham, Ross Barkley and Olivier Giroud also found the net as Thiago Silva and Ben Chilwell enjoyed promising Chelsea debuts.
Speaking after the match, Lampard said: "It was a great exercise for him, another game to see how we want to work off the ball, but also have freedom on the ball and combinations with Tammy [Abraham].
"It's the first of many great nights for him."
Havertz added: "I'm very happy to score my first goal here at Chelsea, I'm very happy about the win and happy about my three goals and I hope we can continue like that."