score:6
It being the Lake District in June, you can expect rain, gorgeous sunshine, fog, wind, calm, hot and cold, so for the first part of your question:
That's the UK for you - very variable :-)
For the second part - I would suggest booking B&B's, especially if the 5 day forecast is good, as the route can get very busy very fast. There is a lot of accommodation along the route, but you don't want to be stuck.