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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.
