Pulisic scored and provided an assist after coming off the bench during the second half of Chelsea's 5-3 Premier League loss to Liverpool on Wednesday.
The United States international, 21, has scored nine league goals and provided four assists in 24 games, comparable to Hazard's first campaign (nine goals and 11 assists in 34 matches) at Chelsea in 2012-13.
Lampard lauded the attacker and said Pulisic's impact on Chelsea was similar to Hazard's, with the Belgian having left for Real Madrid last year.
"He is hugely important. He has had that impact," the Chelsea head coach told a news conference.
"I was here for Eden's first year and it's not easy to come into the Premier League, even for Eden in that first year, and adapt to the Premier League. Christian has had his moments of that.
"Since mid-season he's had a really good patch, since the restart he has been in incredible form. Only the injury he picked up in the Norwich game has kept him out of the [FA Cup] semi-final when he is flying.
"Today he comes on and has 40 minutes, which is great for the injury to feel confident with it and shows the quality that he has been showing. He's so young, he has got such natural talent. He scores goals, he creates goals and he is a big player for us. Delighted to see him come through fit. Clearly he will be a big player for us in these next few games but going forward as well."
Chelsea twice trailed by three goals against Liverpool, who sealed their win late on after the visitors had come back to a 4-3 deficit.
But Lampard had no criticism for under-fire goalkeeper Kepa Arrizabalaga, with Liverpool producing several good finishes.
"I wouldn't talk about individuals in a game where we have conceded those goals. Some were real quality Liverpool finishes, particularly the free-kick [from Trent Alexander-Arnold]," he said.
"There were some collective and individual errors for them but what we did do was contribute towards a really good game. At 4-3 it felt like we would get back into the game. I felt it throughout. At 3-0 it was difficult but even at 3-1 and what that gave us and the way we were playing in the game.
"We know where we're at and we know if we make mistakes like that against a team of the quality of Liverpool, this is what can happen. But there were a lot of good things in the game so I certainly don't want to get into an individual conversation about players.
"We've now got two big domestic games to play this week. It's important we go in together as players, fans, everybody, to finish the season how we want."
With one league game remaining, Chelsea are a point clear of fifth-placed Leicester City, while they will face Arsenal in the FA Cup final on August 1.