I suspect that the Holliday, Holiday, Holyday, Hollyday family came from Syresham Northants, not far from Culworth. I haven't got the baptism indexes after 1750, but a look up might find a James baptised c1775, and looking at marriages it looks like there were Lambs in Middleton Cheney/Chacombe, again not far away, so Catherine may have come from one of those villages.