I've read somewhere that what are commonly called "border pipes" were found all over Northern England, from Cheshire upwards. The 3/2 hornpipes that are associated with Cheshire and Lancashire were originally bagpipe tunes and their popularity dates from a time when the bagpipe was the folk dance instrument of choice.
If there's a bagpipe specific to Lancs, that's a new one on me; I've heard Julian Goodacre and his pipe-playing brothers talking extensively about English pipes and don't remember Lancashire being singled out.
But then, there's very little evidence either way. The discovery of an image of a set of pipes doesn't prove any particular association with the place where that image was found, even if (as in some cases) it was a decorative carving on a church pew.
The Northumbrian smallpipes are the only example which, especially in their modern development, are specific to a geographical area.