March...hmmm - currently we have got good weather. Lake district could be wet on some days regardless of when you go. What do you like doing? are you going with a family? Anyway 8 days, you'll be able to cover a far spread of the place!
Here are some suggestions (and hope you like the outdoor):
Walking/Cycling: so many great walking areas - Great Gable and Langdale Pikes have wonderful scenery........look for the scree faces to run down!!! Waterfalls, grizdale forest park (a fun park with statues that were discovered in 1978)......Guess you should walk up Scafell Pike as it is the largest mountain in England. Get an OS map from the outdoor shops or sometimes from the postoffices. You can get a waterproof one or purchase a map case.
Water: Kayaking/fresh water diving/canyoning (jumping into waterfalls)
Ridges: Sharp edge (great scrammble, knife edge drops, have to have a good head for heights), striding edge (a classic horseshoe with some steep drops and great sites)....although if you have time the best ridge is in North Wales en route to Snowdon
Climbing: Loads of climbing there - get a climbing guide to locate places
Shops: Great outdoor shops in many of the villages (I know Keswick and Kendal) - better to buy out there than in London! Good quality and cheaper.
Science: Then there's the nuclear plant (sella fields). Copper mines in Coniston
Small villages, etc, etc, etc.
Driving - get an OS map that covers the area - there are some awesome gorge by passes. Sorry can't remember what they were called - but very dramatic
Accomodation: Camping (@ 5-7 pounds per night - in a farmer's field - with showers), wild camping is free but is illegal unless you're out in the hills, rent a cottage, or the usual B&B
This should keep you occupied. Have fun