In his third and final year at Oxford, Lynch signed with an agent and appeared in Dunkirk. After graduating, he played Claudio in the Rose Theatre Kingston production of Much Ado About Nothing and Gordon Wilson, the son of the titular character played by Ruth Wilson in the BBC One miniseries Mrs Wilson. That same year, Lynch had a guest role as John-Paul O'Reilly in an episode of the Channel 4 sitcom Derry Girls. He appeared in Wife at the Kiln Theatre in 2019.

In 2022, it was announced that Lynch will appear in a recurring role in the second season of the Amazon Prime Video fantasy series The Lord of the Rings: The Rings of Power.