Pulisic netted five minutes after being brought off the bench in Sunday's 2-1 comeback win at Villa Park as the visitors recovered from a goal down.
The United States international converted Cesar Azpilicueta's cross at the back post to cancel out Kortney Hause's opener, before Olivier Giroud added a quickfire second.
And Lampard expects even more from a fit-again Pulisic, who was making his first appearance since New Year's Day after struggling with a groin issue.
"He was hungry. I know that and I felt for him as I felt for all the players with long-term injuries," he said at his post-match news conference.
"Ruben [Loftus-Cheek] was in the same position, but I know Christian was very hungry. He has trained well. The ability that he has got to arrive in the box is a big thing that I have spoken to him about all season.
"It is the difference between being a very good player off-the-side as an attacking player or the players at the real top level of the game that arrive and score in the six-yard box and hit big numbers yearly.
"I really think Christian can do that so I was pleased with the impact he made when he came on. He will start games for us, of course. I think he is going to be a big player for us, not just in this run-in, but going forward."
Ross Barkley, another who has struggled with injuries, also made a big impression during his 35 minutes on the field and Lampard is pleased with the depth of his squad.
"The players who make the differences should always take all the credit. With Christian and Ross, they came on at the same time and have trained well," he said.
"They both had cases to start but I have some good selection problems. Then you have to consider the type of game and that fitness will play a part.
"Bringing on Christian and Barkley early in the second half was always in my mind depending on how the game went.
"The way it was going we needed a bit of inspiration, Christian with his goal and Ross did as well. I think it shows how important subs are."
Chelsea now hold a five-point lead over fifth-placed Manchester United after winning away from home in the top flight for the first time in 2020.
Lampard, taking charge of his 100th game as manager, acknowledged the importance of picking up a victory in his side's first game back following the three-month hiatus.
"I am really pleased with the performance," he added. "Aston Villa had the chance to [play a game] once before us, but I think we moved the ball well during the game and dominated possession.
"It's been a little bit of our story this season, dominating possession but the need to be more clinical.
"I can definitely give the players some leeway on that one because of the long time off. We showed great quality and character to win the game. I am pleased with the win.
"I think it is important for the group because I think we have seen all the games are looking different.
"It is an obvious statement with the crowds, but in terms of the actual detail of the games and the tempo, the matches, the tiredness factor that has been coming into them too.
"So we didn't know exactly what we were coming into today but now we have three points when some teams have lost points around us."