The indexes show that the Church of Ireland records for Lackagh are at the National Archives of Ireland in Dublin.
The Roman Catholic records for Baptisms and Marriages for 1842 to 1880 are supposed to be on Family Search. It looks as if 1842 is the earliest that survives. Beyond 1880 and all burials are presumably still held by the PP.
It seems that a company called Burkes Bus runs a bus from Galway to Lackagh and on to Tuam (thu via or very close to the ruins) every hour on a weekday, and a restricted Sunday service- https://burkesbus.ie/
It's Transport for Ireland who tells me that the bus stops in Lackagh and all the other stops, not Burkes.
But presumably you will actually have a car. Or will really use a taxi or private car service. But as you asked the question....