That's as may be, but thought we were constrained by these electrification infill proposals being less than 15 miles length. The Morecambe branch is only an additional couple of miles or so needing doing. But would it ever then be worthwhile doing the occasionally-used line on to Heysham. And Carnforth to Barrow-in-Furness is almost 30 miles and so is maybe out of scope for the purpose of this thread. Unless the OP maybe says otherwise.
I think the idea would be to separate these services. Run hourly electric Man Airport - Windermere. Not sure how long that unit could be, as it'll be a prime Man-Bolton-Preston service too.That interworks with the Barrow and Morecambe lines. If you do one it makes sense to do all three
Barrow I would maybe explore 1tph Liverpool-Barrow (bi/wired to Lancaster) - or maybe something like 1tph Preston, 1tph Lancaster to up it to 2tph as a compromise. As I expect on the Barrow-Manchester, many change to go to Scotland, Liverpool, Birmingham and of course London - so journeys aren't probably as geared to Manchester explicitly.
Or try aim for Victoria via Wigan NW perhaps.