Lampard's plea to League bosses came after the Government delivered devastating news to all sports by putting the return of fans on hold because of the coronavirus crisis.
EFL clubs fear they could go out of business unless they get some financial help.
Lampard, who began his playing career with a loan spell at Swansea and also managed Derby before taking over at Chelsea last year, said: “I do think clubs in the Premier League and the Premier League themselves have a heart.
“They understand that and I'm sure as we move forward they will be making positive moves on that front.
“I think it's important that the Premier League as a collective looks at supporting the EFL, the leagues below and grassroots football absolutely, of course. Because that's the base of why we're all here.
“We all started - well I did and (a lot) of the young players started in Sunday league football.
"I've managed in the Championship so I know the difficulties because I was very close with Mel Morris and I understand a lot of the difficulties a lot of the clubs are having."