In reply to yorkshire_lad2:
I think at this time of year it should be fine. The towpath through Lancaster and north up to Carnforth is a recognised cycle path and has in the past been surfaced even if it's pretty messed up now. But south of the city is just a regular earth towpath and is quite bumpy when dry and pretty gloopy in the winter.
The marked cycle Route 6, from Galgate to Conder Green isn't the nicest road as it's narrow and surprisingly busy. Instead, just stay on the canal footpath for a little way beyond Galgate and take the spur canal towpath downhill to Glasson Dock where there are cafe's and icecream.
The old railway line back to Lancaster along the edge of the river is very ridable but a little rougher than when first completed. But work seems to have started on an up grade and the first mile out of Glasson Dock towards Conder Green seems to be being tarmac-ed at the moment.
Keep an eye out on the river and other patches of water as a pretty rare Temminck's Stint has been seen recently.