We plan to visit Keswick, or other areas, in the lake district in late Nov. We will not travel by car. Is it worth the effort due to the weather and questionable public transportation?
Impossible to know what the weather will be like. Might be gloriously sunny or wet and windy or cold and frosty. Snow unlikely at low levels.
Have a look at this blogger's site to see pictures of the Lakes throughout the year.
http://www.loweswatercam.co.uk/Archive_2016.htm
Not sure what you mean by questionable transport? Summer services won't operate but there are buses to get you around.
So yes it's worth the effort.
You might be interested in the programs offered at this country house operated by HF Holidays at Derwent Bank, just outside of Keswick.
https://www.hfholidays.co.uk/country-houses/derwentwater/
The house is right on the lake and offers nice ensuite rooms. All meals, transport, and activities are included. They will pick you up at the Penrith train station and return you there after your stays.
In November they offer 3-night, 4-night, and 7-night stays for guided or unguided walking. Also a ukulele weekend (sounds like fun) and a wildlife-focused program near the end of the month. That one would take you around the Lake District to reach scenic and secluded spots without a lot of walking.
We enjoyed a long weekend here last May and found it very comfortable and well-run. Plus we met some very nice people.
You plan to visit the wettest part of England during the wettest time of the year with relatively short daylight hours. That said, the Lake District can look quite dramatic in winter.
https://weather-and-climate.com/average-monthly-Rainfall-Temperature-Sunshine,keswick,United-Kingdom
I am a huge fan of the Lake District no matter what time of year.
If you plan on going in Nov. though, and you don't like possible wet and gloomy weather, you may want to consider going there at another time. If you are lucky enough to have sunny conditions then the place is spectacularly beautiful at this time of year...clear skies, the ferns and heather are changing color on the fells...maybe a dusting of snow on the tops. Gorgeous!
Public transportation isn't questionable at all in the Lakes. The bus system is very good and will get you to most places you want to go unless they are quite remote. For the remote locations there are shuttle services and taxis you can use. We have sometimes rented cars in the Lakes and other times used the public buses. Either way works well!