Godfrey fractured his fibula after making a challenge on Kai Havertz. He was stretchered off and taken to hospital.
Now the England international is set for a sustained period on the treatment table.
Everton boss Lampard said: “Ben, we are thinking 2-3 months.
“That’s a really quick assessment so we’ll probably find that out in the next couple of days.”
Everton suffered a second defensive blow in the second half of the Chelsea loss.
Yerry Mina went down injured and could not continue.
Lampard is unsure how long the Colombia international may be absent for.
He added: “Yerry, we have no idea. We are assessing that this evening.”