Lake District cycling? Windermere to Keswick?

http://www.bbc.co.uk/news/uk-england-cumbria-43689347

You might find that the road around the east of Thirlmere is closed. I've just looked it up and it says closed until October.  People are working on the hillside above and there is a risk of rocks coming down.

I presume you are intending to get the train from London to Windermere? If so, firstly be aware that the line between Oxenholme and Windermere has been, of late, pretty shite. Numerous cancellations and delays, so much so the local MP called a meeting with Northern Rail to give them an earful!

The A591, which is the main route between Windermere , isn't TOO bad, although in places it is quite narrow and traffic cannot overtake easily, which I treat as 'sod 'em', but you may be different.

From Windermere you will head north out of town, and it's a quick downhill to Troutbeck Bridge, where you can pick up a cycle/pedestrian path to within a couple of miles of Ambleside (this is where the A591 gets narrow, but is a 30mph limit). When in Ambleside, take the lower road (Borrans) as if you are heading to Coniston/Hawkshead, cross over a narrow bridge and take the immediate right (called 'Under Loughrigg') - this narrow road will keep you off the A591 until Rydal, but be aware tourists a can be oblivious to cyclist, if my recent experience is anything to go by. From Rydal it is only a few miles to Grasmere back on the A591.

Coming out of Grasmere on the A591, yes you will have to go over Dunmail Raise, which is a bit of a lump, but nowt compared to some of the climbs we have here, and as has been said before, it's VERY wide going up, enough so that cars and even buses and HGV's can give you easily enough room. There's even room for a car to overtake another without getting even close to the white line. When you crest the top there are two lanes, so again plenty of room, then you are down to one lane as you descend to Thirlmere at Wythburn. You can then take the next left and go round the quiet side of Thirlmere reservoir, which will bring you back to the A591 going into Keswick. You can then either 'suck it up' and go the rest of the way on that road, or double back on yourself slightly, and go via St Johns in the Vale, which is a much quieter (and narrower, obv) road, keep bearing left, and you will go via Castlerigg Stone Circle (our Stonehenge!) and this will lead you to the main road in to Keswick via Chestnut Hill - you're only about half a mile from the centre of town then.

Then enjoy Keswick, it's a lovely little town, but can get quite busy during the main tourist season, obviously. Take time to pedal down to the shores of Derwent water, which is marvelous on a sunny day.

Thinking a bit laterally... could you stay on the train to Carlisle (presumably trains still stop there?), perhaps meeting your southbound friend, and cycle from there? Or from Dalston, which has a station a few miles south of Carlisle on the Cumbrian coast line (that would reduce your mileage to about the same as Windermere-Keswick)?

There are various minor road options to the S/SW of Carlisle to get you to the A66 where you can pick up the cycle path. 

Check out cyclestreets.net - that will sort you out with a very pleasent route. You can choose Fastest, Balance or Quiet. It will give you lovely rural routes on quiet.

Yep, Dunmail is a slog, as are most of the passes, especially in the summer sun as there's no shade. 

Another option is up the Kirkstone pass. But there's more climbing, and whilst the road is quieter than the A591, it can get quite busy. So probably no better overall.

https://ridewithgps.com/routes/27308675

The most peaceful (and remote!) option would be up the Langstrath Valley between Grasmere and Rosthwaite, then round the back of Derwent water to Portinscale. But that’s a significant amount of off-road that would not be much fun on a hybrid.

Dunmail is not going to be the best bit and maybe walk on the verge and push up that mile climb if the traffic is very heavy, still probably quicker/nicer overall than going via Kirkstone. 

There's no railway station at or near Keswick. I don't understand your comment about the trains not running to Penrith, as it's on the main West Coast line. How much would private hire taxi be from Penrith? You may be able to hire a minibus style taxi with fold down seats in order to transport your bikes.
Or have you considered cycling from Penrith to Keswick? My son did it last year in reverse, as part of the C2C and it was entirely on backroads.
The A591 is the main road through the Lakes and can get terribly busy. Dunmail Raise is a slog and whilst wide on the South side, it just means that cars can travel faster. There's even a short section of dual carriageway at the top.
However, Keswick is lovely and has a Booths supermarket. Enjoy.

Definitely doable and a nice ride. Only one busy section that is unavoidable up Dunmail Raise from Grasmere to Thirlmere on the A591. But the road is very wide and there’s good visibility. 

Couple of options:

Mixed surfaces and a ferry crossing (quid a bike):

https://ridewithgps.com/routes/27306473

Paved surfaces, but a bit more traffic:

https://ridewithgps.com/routes/27306523

The missus and I cycled Grasmere to Keswick and back on our mountain bikes last year. That route is lovely, but a bit rough so I'm not sure how easy it would be on hybrids. The main road going between the lakes (A591?) is very busy so I'd keep away from that if at all possible.