Kilmore is the name of a civil parish in northwestern Mayo, and you can find more info about it at this link (where there are further links to info about the various townlands within the parish, which are numerous)
It is located within the Catholic parish of Kilmore Erris (Erris is the name of the traditional "Barony" covering that area, which is of purely historical interest these days). The National Library of Ireland has many Catholic parish registers available online, but the ones available for Kilmore Erris only go back to 1860. They're available at this link:
It can be very hard to find records of people born that long ago in some parts of Ireland. I looked for him in the Family Search database, but saw no likely candidate. The closest was a Thomas William Lavell born in 1818, but he lived in Achill, to the south of Kilmore.
The Lavell/Lavelle surname is an anglicization of the Irish surname Ó Maolfhábhail, and originated in northwestern Mayo, although it is also found in Donegal. It was sometimes anglicized as Melville or (in Donegal) as Fall.