I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN county, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
Aughrim is in Co. Roscommon.
For Mary Fitzmaurice M 1866 +/- 4 yrs somewhere in Ireland, I found 21 rcds: 9 MAYo, 8 ROSscommon, 3-LIMerick, and LONgford.
For Laurence Lynch M ditto, I found 11 rcds: CRK, WSM, 4-WIK, LEI, and 4-ROS.
Within Co. Roscommon, I found matching M rcds for Laurence and Mary in 1866, Kilbegnet/Ballinakill parish. These are likely for your ancestors. A view of the detailed M rcds SHOULD show they married each other. If so, this validates the rcd.
For Laurence Lynch B ???? in Co. Roscommon with a father forenamed Laurence, I found 4 rcds: 1873, 1875, and 2 1882. Parishes areDysart/Tisrara, Ardcarne/Cootehill, Brideswell CP, and Dysart/Tisrara respectively.
For Marg(aret) Lynch B ditto, I found 3 rcds: 2-1873 and 1886. Parishes are Brideswell CP, Dysart/Tisrara, and Taughmaconnell respectively.
For James Lynch B ???? ditto, I found 0 rcds.
For Hannah Lynch B ???? ditto, ditto.
For Ann(ie) Lynch B ditto, ditto.
Sources indicate 4 RC parish rcds haven't been digitized: Ballinafad, Ballinlough, Cloverhill, and Strokestown. Also Creagh civil rcds haven't been digitized. These are held at the center email@example.com.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.