I'd alight for the Lake District at Penrith station. Oxenholme station is further away from your destination and a bit out in the sticks. I remember being glad I had my bike when I was last there. I agree Keswick is a tourist trap/hub but as you don't have transport of your own it'll be a better place to find accommodation and transport to take you the short distance to Low Lorton.

I've been to the area many times over the years and had all sorts of weather although it's no coincidence that Keswick is such a great place to buy rain wear!!