You could always get the train. The Transpennine express will take you back to Manc from Ncl and you don't need to book bikes on. You can also get to the start - Whitehaven usually - by train via carlisle.
Regarding your luggage, when we did LEJOG, one of the things we did was leave supplies at certain places where we were staying en route. We rang up first, and then either dropped them off by hand or posted them. They were B&Bs/hotels though but were very obliging. We made sure we asked though.
To be honest, if you're doing it in 3 days, you could probably get away with a seatpost mounted bag on your road bike. You're only going to need basic toiletries and a small bottle of handwash liquid to do your riding clothes each night, your usual tools (put these in a second bottle mount in your frame), and some light clothes for the evening. Don't bother with a second pair of shoes - just wear the ones you ride in and a T-shirt / lightweight trousers can roll up pretty small.