[6] In October 2020 he made his Premiership debut against Leicester Tigers and later that season scored a try during Harlequins 43–36 defeat of Bristol Bears in the semi-final, a game in which Quins recovered from 28 points down to win.

[6][7] The following weekend on 26 June 2021 Lynagh scored two late tries as Quins defeated defending champions Exeter Chiefs 40-38 in the final at Twickenham to win their first Premiership title for nine years.

[9] In January 2024, although not originally named in the match day squad, Lynagh started on the bench for Harlequins in their Champions Cup pool stage fixture against Ulster because Cameron Anderson was injured.

[10] During the same European campaign, he was part of the side that defeated Glasgow Warriors 28-24 at home in the Round of 16, the first time the club had ever won a knockout game in the competition.

In February 2024, he received a call up to the Italy squad by head coach Gonzalo Quesada for the 2024 Six Nations following the announcement of his move to Benetton at the end of the season.