I think the census entry is Sawley, which is a small village & the site of an Abbey about 4 miles NE of Clitheroe. It was an Extra Parochial area of the West Riding of Yorkshire meaning it didn't have its own parish. (Not to be confused with Sawley Nr Ripon). Residents there would have gone to one of the surrounding parishes for Baptisms & marriages.
The area where Lancashire & Yorkshire meet is very confusing for research - I have family from there and have had to work hard to find where the records are now kept.
Sawley seems to have become part of the parish of Grindleton in 1844, so that may be a place to look - their Parish Records are at Lancashire Records Office (back to 1744)