IMO the best riding in the lakes is the lower level stuff around the south western lakes, Grizedale, Satterthwate, High Oxen Fell/Skellwith, Claife Heights etc. Given the time of year and what the weather will be like, this area might be the best option anyway.
The riding around there doesn't have the big mountain feel to it that is such a big part of riding in the lakes (the 'big pass' rides like Walna Scar, Nan Bield, High Stile, High Street etc, are all amazing rites de passage type rides, but they could be miserable in fowl weather), but the tracks are great fun, perhaps offering more technical riding, accessible and close to civilization should the sky decide to fall in on your head!
Base yourself in Ambleside (the Ambleside YHA is great, cheap and has family rooms. It also happens to be where i met my wife so it has a special place in my heart!). This will give you access to everything you need including a cinema and a great bike shop. Bike Treks will help you locate the best trails.