Lancashire was the site of a Quidditch match in 1385 that didn’t go too well for the local team. An Irish team from Cork beat them soundly and the fans of the Lancashire team chased the Irish players out of town (QA8).
Lancashire is quite possibly where the Longbottom family are from (Lexicon essay by S Hall).
From the Web
Lancashire is one of the old counties of England, on the northwest coast. The area was the heart of the Industrial Revolution and it is the location of the famous Blackpool Pier. Its Wikipedia page, however, does not make any mention of wizarding activity (Wikipedia).