The 19-year-old played his sixth game of the season in the 3-1 win over Luton Town in the FA Cup fourth round.
While he may get more chances in the cup competitions, he may even go out on loan to get regular game time.
Lampard will keep his options open regarding Gilmour's immediate future.
He told reporters post-game: "At the moment, he won't go on loan but we will keep it open until the end of the month."
Asked about Gilmour's performance in the Luton game, Lampard added: "His comfort on the ball, the way he moved it, his discipline, his personality was great. If he plays like he does today, it makes it very difficult for me not to give him a run. He trains that way too.
"With his youth and the injury he had, and with the difficult run we've been on in the last month, it's been a case of me finding the right time to get Billy in. Today felt like the right time and he was brilliant."