The new campaign is set to begin on this date due to the impact of the Covid-19 crisis that forced this season to be suspended for three months.
But Lampard believes this is unrealistic for his side because their current season is still ongoing and has been extended by two weeks at least.
The Blues must travel to Germany to face Bayern Munich in the Champions League on Saturday, having lost this weekend's FA Cup final to Arsenal and seen Cesar Azpilicueta, Christian Pulisic and Pedro all limp off injured.
Lampard's men trail 3-0 from the first leg of the last 16 tie and are expected to go out.
But whatever happens, Lampard admits he fears for the health of his stars and wants the Premier League to give his club more time to rest before it all kicks off again.
He reckons it would be unfair if the Blues were made to start on the same date as everyone else and he said: "I am guessing we will be told when we start and that will be dependent on how we go against Bayern Munich.
"I am not forgetting the game against Bayern as that is a big game for us, but the players need to be given a break to play at the level and the quality of the product that the Premier League is.
"Even in a worst case scenario and we don't go through against Bayern, the 12th feels too early for me for the players to start playing again.
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"The players need a break. That is why we have pulled two hamstrings (in the FA Cup final) and had players pull out of the game before this.
"I would like to think the Premier League would look seriously at that and hopefully give us a fair start next season. We deserve to be, as a Premier league club, competing in the Champions League."
Lampard, meanwhile, admits Willian could have played his last game for the club and insists there will be no hard feelings if the Brazilian leaves Stamford Bridge this summer.
He added: "It is his decision. I have not got that answer. I know the situation from the club's end.
"I have a great relationship with Willian. Of course I am very happy with Willian as he has been brilliant for me this season with his input and work ethic within the squad.
"But it is his choice and I respect his choice. He has been a great servant for Chelsea if he decides to move on. And if he does decide to move on then Chelsea moves on as well and we have to look forward ourselves."