@miriamshoshana See I was briefly confused as well and then I remembered that Mr Darcy lives in Derbyshire. So in the films while they still didn’t go to the Lake District, they went to the Peak District, in Derbyshire (though I’m not sure if that was specified in the books).
Long story short, Derbyshire is a strange place in the Midlands that looks like it should at least be in Cumbria if not on the other side of the border or in Wales, but it’s very pretty so if it was decided that Lizzie and her aunt and uncle were going to Derbyshire insead of the Lakes, they would go to the Peaks instead.
(Derbyshire is Middle Earth. Quite literally given it’s a land-locked county in the middle of England that looks like this, it’s a very confusing place. Though it makes more sense when you remember it’s next to Yorkshire, albeit the southern part. But it’s still…wrong. I love it.).