Goals from Mason Mount, Emerson Palmieri and two goals from Olivier Giroud handed Lampard his first win as the Blues' boss.
But after the game, the Chelsea legend picked out academy star Gilmour as one of the players who has impressed him in this preseason campaign so far.
Gilmour, 18, played 45 minutes on Saturday versus St Patrick's, and also featured in the Blues' first pre-season game against Bohemians.
'He's been great!'
Speaking to Chelsea TV after the game, Lampard singled out the Chelsea youngster for some very much deserved positive feedback on his performances so far in this preseason.
“[Billy's] had a brilliant trip and has shown real personality at the level that he’s played for a young lad in these two games.
“He’s been great. I just hope Billy keeps pushing on with that this season.”
The Gilmour debate
With Gilmour impressing so highly in pre-season so far, it raises the question whether or not Lampard should include him in the first team squad this season.
Is it too early? Does he need a loan move? Or does he need to remain patient and develop further in the academy set-up? These are all questions the new Chelsea boss will have to take into consideration.
He is still only 18-years-old, the same age as Callum Hudson-Odoi, so there is no need to rush his introduction.
This topic has also created a lot of debate amongst the Chelsea fanbase on social media.
Always been a big fan of @billygilmourrr & thought he was one for the future. But so many of my fellow Chelsea fans, believe his ready now. What do you guys think? Should Lampard give him a chance this season & ship 1 or 2 of the other midfielders out? #CFC pic.twitter.com/gTW5pwiHmg— Frank Khalid (@FrankKhalidUK) July 14, 2019