I searched the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Lynch is a VERY common name.
For Thomas Lynch B 1830 +/- 5 yrs, somewhere in Ireland, with a father forenamed John, and mother Mary, I found 9 matching records. You will need a more exact DOB, and/or placename to help you pick which, if any, is the correct record.
Note - 1830 is EARLY for Irish records. Many B/M/D records before 1850 either weren't recorded, or haven't survived.