The 21-year-old had been in sparking form since the restart but limped off during the second half of last weekend's FA Cup final defeat to Arsenal.
A subsequent scan has shown damage which Lampard estimates will take around six weeks to heal, ruling the United States international out of Saturday's Champions League last-16 second leg clash against Bayern Munich and making him a major doubt for the subsequent campaign.
The Premier League is due to begin again on Sept. 12 but clubs engaged in European competition are likely to start later. The Blues are unsure at this stage when their first fixture will be but Lampard said: "With Pulisic, it's touch and go for the start of the season. We have to treat it right. He has been fantastic although had a couple of these injuries this season.
"In the big scheme when Pulisic reflects on the first season, I think his improvement levels coming here, when you think of his goals and assists being the best of his career in the first year in the Premier League, from where he was at the start and how he was playing in restart he should be very happy because that is down to his work.
"We will get him fit and ready. If he misses the first part of the season, the first one or two games, then we will have a firing Christian hungry for restart."
Chelsea are also without Willian in Germany due to injury as he closes in on a free transfer to London rivals Arsenal.
Lampard had been pushing the Blues to offer the 31-year-old the three-year deal he had requested but insisted the Brazilian's departure will not be acrimonious.
"I haven't got an answer for you first and foremost because Willian remains our player at the moment," said Lampard. "He is injured. He was injured for the cup final and injured for tomorrow and he would have given everything to play in those games. I know Willian well and I've seen him, he's carried this injury in the latter part of the restart.
"In terms of being disappointed, certainly as a club we've done everything we can to explain to Willian... mine and his relationship is really close and I would have no feeling of disappointment if he does move on.
"I've played with him, I've coached him. He's a fantastic man and a fantastic player. I think he will feel like that about Chelsea. I'll leave him to say his own words but I don't want anyone to try and find a negative attitude. The club have acted very well in this as well. If he moves on I personally will wish him well. That is where we are at.
"I think he leaves a hole as a player who has been here for I think seven seasons, being part of successful teams. When I came in and we had a lot of issues in terms of younger players, players back from loan, transitional elements to the group, Willian was one you looked at and relied on in terms of his experience and quality. He has shown me that all year.
"He has his own decisions to make. We as a club will always want to move forward, no matter what. Eden Hazard left last year, the club continues to work in a forward direction which I think we have in many ways. That remains the same, whatever player leaves the club.
"When a player is out of contract they have the freedom and the right to play wherever they want. You have to understand that if they stay in the league and it is a player of Willian's quality for instance, then they will go and contribute to that team. We have to accept that and move on. I have no problems with that."
Blues defender Antonio Rudiger admitted his regret at Willian's imminent departure.
"He is a man of himself and he makes the decision for himself," said the centre-back. "I don't know the situation but if he goes that will be for us and me a huge loss because I think after the restart people could see that he is very important for us in the team."
No team has ever won a Champions League knockout tie after losing the home leg 3-0 and after securing qualification for next season's competition by finishing fourth in the Premier League, Lampard added: "It has been a long season for us, successful in many ways. And now we have a huge challenge in a one-off game to try and do something special.
"I understand the difficulties of the game. All I want to see is a performance and attitude from the team that attempts to do something special. It will be very difficult. I don't have to pretend that with the players."