Lower league clubs face crippling loses after the government confirmed that plans to allow some fans to return in October had been scrapped as virus cases rise across Britain and Lampard feels that the top-flight has a duty to help out.
The Chelsea boss said: "I think it's important that the Premier League as a collective looks at supporting the EFL, the leagues below and grassroots football, absolutely.
"That's the base of why we're all here. I started and [a lot] of the young players started in Sunday league football. I've managed in the Championship. I understand a lot of the difficulties clubs are having, so I think there certainly can be a conversation."
Lampard feels that Premier League clubs will have "a heart" in terms of helping out their lower-league counterparts.
He said: "I can't go too political because I don't know enough about the numbers, but I do think clubs in the Premier League and the Premier League themselves have a heart. They understand and I'm sure as we move forward they will be making positive moves on that front."
However, Burnley manager Sean Dyche was less enthused by the prospect and questioned whether it would be done in other industries.
He said: "There's lots of different businesses out there making huge sums of money that could therefore protect similar lines of business, but lower down. If you are going to apply it to football, I think you have to apply it across the country to everyone and every business."