John - just spotted this post!
All I have, I am afraid, is a date in the PR of 1704 which describes John Lowther as 'of Greystoke mill'.
His predecessor there was probably John DOWSON (1655-1682 - I can't find any other millers mentioned in between) and his successor seems to have been Nicholas DARRACK (1717-1720) (according to TNA)
My own family started it's connection with the mill c 1760, ending c 1930 (ROUTLEDGE, ROBINSON, GRAHAM)
I would be interested in anything you have on John LOWTHER's time at the mill.
Andy