Even on a Bank Holiday weekend you will find the roads pretty quiet away from the tourist honeypots.
Roads are in pretty good condition - better and fewer potholes than you are used to in London. They are narrow though.
The main A roads into the Lakes - A590/591 and A66. Ambleside, Windermere and Bowness tend to get very busy with traffic and tourists but they are small, you are just passing through and they have some good cafes so don't bother too much about avoiding them.
Just be aware the Lakes are hilly with some big hills and some long hills. There are lots of quiet back roads you can enjoy, the tourist drivers tend to be on holiday and therefore patient in passing but the off-road tracks/bridleways you might be tempted to take can be quite rocky so best not for touring. Save them for the mountain bike.
Oh and the lakes are there for a reason - it rains a lot - so be prepared.
My daughter's favourite poem for the Lake District:
It rained and it rained and rained and rained,
The average fall was well maintained,
And when the tracks were simply bogs,
It started raining cats and dogs.
After a drought of half an hour,
We had a most refreshing shower,
And then the most curious thing of all,
A gentle rain began to fall.
Next day was also fairly dry,
Save for the deluge from the sky,
Which wetted the party to the skin,
And after that the rain set in.