Born in North Belfast, Lynch became a republican activist around the start of The Troubles, and sided with the Official wing of Sinn Féin in the split of 1970. He was imprisoned from October 1971 until the following year. He was a strong supporter of the Official IRA's ceasefire in 1972 and Official Sinn Féin's vocal socialism. As a result, he became active in the Republican Clubs movement, and stood for the organisation in Belfast North at the Northern Ireland Assembly, 1973. He received only 1.7% of the first preference votes cast and was not elected. He stood again for the Northern Ireland Constitutional Convention, but his vote dropped to just 1.3%. He was elected to Belfast City Council in 1977, representing the G district, but lost his seat in 1981.
Lynch next stood in the Westminster seat of Belfast North at the 1979 general election, increasing his vote to 4.5%, the best result for Republican Clubs in Northern Ireland, and at the Northern Ireland Assembly election, 1982, he increased his share to 7.1%.
In 1982, Republican Clubs was renamed the Workers' Party of Ireland and Lynch became its Northern Chairman and national Vice-President He then stood in the 1983 general election, receiving 5.7% of the vote, but did less well in the Northern Ireland-wide European Parliament election in 1984, taking only 1.3% and seventh position of eight candidates. He was re-elected to Belfast City Council in 1985, representing Oldpark, and held his seat in 1989.
Lynch's best result in a Westminster election came when he took 11.8% of the vote in a three-way contest in the Belfast North by-election, 1986. At the following year's general election, he dropped back to 8.3%. He also stood in the 1989 European election, placing eighth out of ten candidates.
In 1992, Lynch sided with the split from the Workers' Party which produced Democratic Left, and he became the new group's main figure in Northern Ireland. Standing for the new organisation, at the 1992 UK general election his vote fell to 3.7% and he lost his council seat the following year. His last contest for the party was heading its North Belfast list for the Northern Ireland Assembly election in 1996, but the list took only 123 votes. Democratic Left dissolved in 1998, its members invited to join the Labour Party but not permitted to organise in Northern Ireland.
- "Pain will linger in Ireland", Buffalo News, 21 May 1998
- Ian S. Wood, Crimes of Loyalty
- Local Government Elections 1973-1981: Belfast, Northern Ireland Elections]
- North Belfast 1973-82, Northern Ireland Elections
- North Belfast, 1983-1992, Northern Ireland Elections
- The 1984 European election, Northern Ireland Elections
- The 1989 European elections, Northern Ireland Elections
- Oliver McGuckin, "Paul leads the charm offensive", Belfast Telegraph, 30 May 1996
- Belfast City Council, 1993-2005, Northern Ireland Elections
- 1996 Forum Elections: Candidates in North Belfast, Northern Ireland Elections
- Steven King on Thursday, Steven King, Belfast Telegraph, 17 December 1998
- Belfast police groups select leaders, Jonathan McCambridge, Belfast Telegraph ,17 April 2003
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