Pulisic has netted three goals in seven league outings since football's resumption, with the USA forward boasting a new sharpness.
Blues boss Lampard revealed the 21-year-old had seized on the coronavirus lockdown as a chance to graft away on his conditioning, and the results have been almost immediate.
Now Lampard wants the former Borussia Dortmund player to boost both his goals and assists tally, in order to reach his peak.
"I have seen a real improvement in his all-round game," said Lampard, of Pulisic.
"Coming to the Premier League is very difficult because of the physical nature of the league and we have to remember how young he is and the summer he had.
"I think he found those physical demands pretty strong in the beginning and now you are seeing him deal with it better. A lot of that can be credit to himself and how he has approached it.
"He has worked a lot with our strength and conditioning coach, Adam Burrows, who is fantastic. They have worked a lot together, but it is Christian who has to take on that responsibility and he has. Physically that has helped him.
"Also, just his talent is coming through. Looking forward I probably want to see more of what he has shown in recent times, which is goals and assists, because that is what the best in the world do in that position.
"I feel he has the capability to do that as he improves. That can be the edge as his game goes on and moves on levels."
"It wouldn't fall short on me the pride of being able to walk out the club that I love at Wembley, even for a semi-final," said Lampard.
"It's a huge game against Manchester United, so I'll be very proud on Sunday. It was obviously a fantastic feeling to win the cup as a player.
"I was fortunate enough to win it, and I grew up on it and seeing those wins for my dad in 75 and 80, so I had a strong feeling of what the FA Cup's about and that's never changed for me as the years have gone by."