As mentioned Lake District and cheap is virtually never heard of, and if it is then be worried. Camping is by far the cheapest option but remember it isn't called the Lake District due to it's dry weather! :-)
So firstly you need to work out what kind of accommodation you want, then work out what transport options you've got. Three more sites that might help cover all bases...
http://www.ukbed.com/cumbria+lake-district/
http://www.ukcampsite.com/cumbria+lake-distric t/
http://www.ukcottage.com/cumbria+lake-district /
The first one covers hotels & B&Bs with the latter being cheaper usually. Cottages might seem expensive, but if you compare them to a week in a hotel they often work out cheaper, especially when you consider the cost of eating out in the lakes.
If you want cheap, my advice would be to stay outside the national park. Kendal and Penrith are cheaper but very close to the national park for example, whereas Ambleside, Windermere and Keswick are within it, but you're paying for that.
If you've got a car then there are plenty of options and remember that Cumbria isn't just the Lake District. There's things away from it like Hadrians Wall, Tullie House Museum in Carlisle, Holker Hall near Grange-over-Sands.
A few attractions around the lakes:
http://www.aardvarkurl.net/u/n8fo5v
(redirects as original URL is too long)
I must admit, the Lake District in Summer isn't exactly my favourite place, but that's mainly due to all the annoying kids and caravans, but even September can be good as most attractions will still be open and the kids