Keswick doesn't look too good for the month of March. Is it worth a trip with no car????
March certainly isn’t the month that gives the warmest, driest weather of the year, but with the right clothing, a trip there is certainly possible. It maybe rainy and snow is possible.
Personally, I never visit the Lake District without a car, as I prefer Eskdale and the western Lakes that are difficult to access without a car. Certain areas of the Lakes are accessible without a car.
Several house museums in the south lakes that close for the winter are open again in March. Some bus routes restart from Easter or early April; see www.stagecoachbus.com for schedules.
It will still be wintry but the Lakes are beautiful no matter the season in my eyes. As long as you stay on the main routes the buses will still be running. More outlying areas are more difficult that time of year. A car will certainly make it easier and the roads won't be nearly as congested as they tend to be during the height of the tourist season. I wouldn't hesitate to go!
I read a book - AGES AGO - part of which was set in Keswick. I'd be tempted to go there at any time of year. That's just me, though. I like to visit places I've read about.
When you ask if it's worth a trip -- from where? Are you going to be in the north of England anyway, or would this be a dedicated trip from London, or ... ?
Personally I can think of dozens of other places nearer to London that would be enjoyable to visit. OTOH, if you're a big fan of the lake district and its historical associations, Keswick may be a high priority for you. The town is pretty and has a number of historical markers indicating which famous person did what famous thing where.
As noted on this web page, the nearest railway station is Penrith, which is a nice non-touristy town, IMO. Narrowbar is a great place for lunch and the town has a helpful TI office. You'd get to Keswick by bus, which takes about 40 minutes. https://www.keswick.org/visitor-information/getting-to-keswick
See my answer on your other (more recent) thread:
https://community.ricksteves.com/travel-forum/england/lake-district-in-march