From the longer Wikipedia page [1], which has a fuller list of High Sheriffs:

Westmorland (sometimes spelled Westmoreland) in North West England no longer exists as a county, the original core of it having merged into the modern district of Eden within the county of Cumbria.

The traditional county of Westmorland, like neighbouring Lancashire, was itself a new creation during the Middle Ages. It seems to have been treated as part of Yorkshire in the 11th century, and the eventual boundaries represented a merger between an earlier entity called Westmorland, and the Barony of Kendal, which was apparently originally considered part of the Honor of Lancaster, though it did not become part of Lancashire. Kendal is also now part of Cumbria.

The high sheriffs of the period were: