Try searching the VWML digital archive and the Roud indexes on the VWML site: VWML. The indexes use historic county names and using the advance search facility to search on Cumberland OR Westmorland gives 675 results. The only way of searching for places in Lancashire North of the Sands is to search for places like Barrow or Ulverston individually.

Or you can use the map search. Click on the map on the library home page and zoom into Cumbria. Places where songs were collected are marked by red pins. You'll need to be very patient as it takes a long time to download all the information.