The Blues lost Saturday’s FA Cup final 2-1 to London rivals Arsenal but are still not finished with the current campaign.
Lampard’s side take on Bayern Munich on Saturday in the rescheduled second leg of their Champions League round-of-16 tie, trailing 3-0 from the first leg.
Even if they exit the competition, Chelsea will have just 35 days before the new season is due to begin.
Manchester City are also still in the Champions League, the final of which is scheduled for August 23, while Manchester United and Wolves are involved in the Europa League, which ends on August 21.
It is understood that when Premier League clubs agreed a September 12 start date, it was also clear there would need to be at least a 30-day break for Chelsea and any of the other teams playing in the end-of-season European competitions.
Lampard lost Willian and Ruben Loftus-Cheek on the eve of the FA Cup final to injury and Cesar Azpilicueta and goalscorer Christian Pulisic during the game to hamstring problems.
“Even in a worst-case scenario, we don’t go through against Bayern, the 12th feels too early for me for the players to start playing again,” said the Chelsea boss.
“The players need a break. That is why we have pulled two hamstrings and had players pull out of the game before this.”
Lampard implored the Premier League to make sure clubs start the next season with a level playing field.
“I would like to think the Premier League would look seriously at that,” he said.
“Hopefully they give us a fair start next season. We deserve to be (given a fair start) as a Premier League club competing in the Champions League.”