Since there is little prospect of either the Barrow or Windermere lines being electrified anytime soon, could it be a smart idea for Northern to consider either removing the service completely, or alter it so that it becomes a portion working between Preston and Lancaster; a 331 off one of the Manchester-Blackpool services?
Having a DMU running all way from Manchester Airport to Carnforth/Oxenholme under wires isn't particularly good, so this would remove this problem. Also it'll save a bit of money for Northern without impacting on travel convenience too much and it'll free up another path along the Castlefield line. Bolton and Chorley won't actually lose a service compared to now as it still currently runs via Wigan.
The Oxenholme-Windermere shuttle could be operated by a 769 or 195, likewise the Lancaster to Barrow shuttle. Ideally a half hourly Lancaster to Manchester frequency would be retained by using a 331 off the Blackpool service, detaching at Preston. But if Lancaster isn't suitable for turning back then you can probably get away with an hourly Lancaster to Manchester frequency (the TPE Scotland).
Perhaps TPE themselves could use an 802 diagram and remove a couple of Scotland services to instead provide two direct services per day between Manchester and Windermere, running in the existing Scotland paths.