The 19-year-old midfielder has enjoyed a fine breakthrough campaign at Stamford Bridge but will not feature again this term.
The Scot started Chelsea’s 3-2 Premier League win at Crystal Palace on Tuesday but was replaced in the closing stages by Jorginho.
“Billy Gilmour has had an operation on his knee this morning, so he will be out we estimate somewhere between three and four months unfortunately,” said Lampard.
“I’m obviously very disappointed as we all are here and of course Billy himself.
“I spoke with him yesterday at length, and giving him support. He’s a tough boy, it hit him hard especially as a young boy who has just made a breakthrough.”
Lampard, speaking to the press ahead of third-placed Chelsea’s match against Sheffield United on Saturday, praised Gilmour for the impact he has had this season.
“His character for me is fantastic, particularly with his age, to get himself around the first-team squad and push himself into the team,” he said.
Italy midfielder Jorginho could start his first match since football’s resumption at Bramall Lane. N’Golo Kante will miss out again due to a hamstring issue.
Former Napoli player Jorginho is understood to be wanted back in Serie A by Juventus and has found himself down the Blues’ pecking order since the league’s restart.
But Lampard said the 28-year-old had nothing to prove to anyone at Stamford Bridge.
“He proves it in training and when he plays for me,” he said.
“I hope there isn’t a point to prove as such, I just want to see the usual Jorginho.”
When asked whether Jorginho would be a Chelsea player next season, Lampard added: “I keep getting asked about next season, but it’s irrelevant to me. These final few games will define how we sit and look at this season and look forward to next.”