Finn joined the Bruff club at a young age and played in all grades at juvenile and underage levels before joining the club's top adult team. On 25 October2014, he won a Premier Intermediate Championship medal following a 2-14 to 0-16 defeat of Croom in the final.
Inter-county
Minor and under-21
Finn first played for the Limerick minor hurling team at the age of seventeen. On 23 July 2013, he was at left corner-back when Limerick won their first Munster Championship title in 29 years after a 1-20 to 4-08 defeat of Waterford in a replay of the final. Finn was eligible for the minor grade again the following year and won a second successive Munster Championship medal after a 0-24 to 0-18 second successive defeat of Waterford in a replay of the final. On 7 September 2014, Finn was at right corner-back for Limerick's 2-17 to 0-19 defeat by Kilkenny in the All-Ireland final. Finn subsequently joined the Limerick under-21 hurling team and won a Munster Championship medal in his first season after a 0-22 to 0-19 win over Clare in the final. On 12 September 2015, Finn was at right corner-back when Limerick defeated Wexford by 0-26 to 1-07 in the All-Ireland final. On 4 February 2016, Finn was ruled out for the year after tearing his cruciate ligament. After returning to the panel in 2017, Finn won a second Munster Championship medal after a 0-16 to 1-11 defeat of Cork in the final. On 9 September 2017, Lynch was at right corner-back in Limerick's 0-17 to 0-11 defeat of Kilkenny in the All-Ireland final. He was later named on the Bord Gáis EnergyTeam of the Year.
Senior
Finn was added to the Limerick senior hurling panel in advance of the 2016 National League, however, a cruciate injury ruled him out for the year. On 4 March 2017, Finn made his senior debut at right corner-back in a 1-25 to 3-15 defeat of Offaly in the National Hurling League. Later that season he made his first championship appearance in a 3-17 to 2-16 defeat by Clare. On 19 August 2018, Finn was at right corner-back when Limerick won their first All-Ireland title in 45 years after a 3-16 to 2-18 defeat of Galway in the final. Later that day he was named on The Sunday Game Team of the Year. Finn ended the season by winning an All-Star Award. On 31 March 2019, Finn was selected at full-back for Limerick's National League final meeting with Waterford at Croke Park. He collected a winners' medal following the 1-24 to 0-19 victory. On 30 June 2019, Finn won a Munster Championship medal at right corner-back following Limerick's 2-26 to 2-14 defeat of Tipperary in the final. He ended the season by being named in the right corner-back position on the GAA/GPA All-Star Team.
Career statistics
Honours
;University of Limerick
Fitzgibbon Cup : 2018
;Bruff
Limerick Premier Intermediate Hurling Championship : 2014