Robert Morden, detail from map of Lancashire from Camden's Britannia newly translated into English by Edmund Gibson ... (London, F. Collins for Abel Swale, 1695).

When Fox says he is 'going into Cumberland', he means that he is crossing the Duddon to the old county. The South Lakes area, now in Cumbria, was 'Lancashire north of the Sands'. Ulverston and Swarthmoor were thus in Lancashire, as were Dalton and Kirkby-in-Furness. Miles Wennington's (Ash House) was just over the border.
In this map, modern Cumbria is divided between three counties: reading left to right, Cumberland (green border), Lancashire (yellow border), and Westmorland (red border).

Image © Meg Twycross 2016