In reply to bigbobbyking:
There is the Guild Wheel cycle route that forms a loop around Preston which is a nice traffic free, but slightly tortuous way to avoid the centre. I think it is cycle route 622.
Depending on your route north of Preston you can follow it either way around from the South side of the city. Personally I'd look at looping around East to Longridge then going via Harris End & Quernmore to Caton. Then through Over Kellet to Carnforth & Warton. A beautiful hilly route on quiet roads
A flatter alternative is to take the Guild Wheel West, and head north to Lancaster via Great Eccleston etc. Or, not as bad as it sounds is to pick up the A6 north from the centre of Preston and just tap it out up to Lancaster. Busy but lots of cyclists do use it and there are some cycle lanes.