Might be something to do with the famous, Jonathan Dodgson Carr...1831 left Kendal for Carlisle where he set up his own flour mill and bakery.
Although the, 'so named', Millers Moss doesn't appear to be on the Kendal to Carlisle 'Millers Way' Route/Walk, Millers Moss might have been named after him, for some romantic reason.
He also set up a flour factory in Silloth.
There's also a 'Millers Way 2' walk from Carlisle to Silloth.