At a guess (I haven't ever had to do this): Bus from Keswick to Kendal; train from Kendal to Lancaster (there's no main line stop at Carnforth any more); train from Lancaster to Barrow; train from Barrow to Foxfield. Then you need to walk or arrange a taxi. The last train leg might be done in reverse from somewhere like Whitehaven to Foxfield so you'd just need to get to Whitehaven.
I've no idea if any of the above actually link up and it might take you longer than the traverse itself.