Chelsea cruised past Barnsley at Stamford Bridge on Wednesday, with Havertz firing a hat-trick in the 6-0 win over Championship side.
Havertz was joined on the scoresheet by Tammy Abraham, Ross Barkley and Olivier Giroud as Chelsea ran rampant in a match that saw summer additions Ben Chilwell and Thiago Silva make their debuts.
Following an opener from Abraham, Havertz fired three of Chelsea's next four goals with Barkley's 49th-minute finish sandwiched in between the first and second.
Havertz's goals were his first in a Chelsea shirt, having struggled in his first two games after the club completed his £70 million ($91m) move from Bayer Leverkusen.
Lampard admitted that he nearly took Havertz off just before he completed his hat-trick, although the Chelsea boss admits he is glad he didn't.
"Perfect game for Kai today because he came here without hardly any training," Lampard told his post-match press conference. "We had to throw him in because we had injuries in attacking areas.
"Tonight was a great progression, for him to play this game. His work rate, he helps Ross Barkley score his goal, his tackle in midfield in a high area and he gets his three goals in good quality. There's only going to be more of that.
"I predicted it. I wanted to protect him at that point. The idea with Kai tonight was to give him a training session. To not disrespect the game, but for him personally, to see how we play, to work with his teammates, get on the pitch, see how we want to press, be part of that.
"When we have the ball, there's much more of an element of freedom for a player of his quality. He did everything we wanted from him tonight."
He added: "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."
Next up for Chelsea will be a trip to West Bromwich Albion on Saturday before the Blues return home to face Crystal Palace in their fourth Premier League match of the season.