Cannondale carbon synapse rear cassette size increase. I'm a 66 year old, 6 ft 3 inch (190cm)  18 and 1/2 stone (117kg / 259 lb) biker ! 

I own a cannondale carbon synapse with a 32 tooth cassette on the rear wheel that was okay for Mont Ventoux climb last year. This year our group of skinny bikers ( I'm the heaviest by 4 stone) are planning all the passes in the Lake District over 4 days.

Can I put on a 36t cassette without changing all the front chainrings and chain as long as I keep the same number of cogs on the rear cassette i.e. 8?
These are serious climbs:


Cycling in the Lake District – Leave the big ring at home
Eight iconic climbs of the Lake District


Not high, but hard, some with gradients of 25% and even 33%

Kudos for Mont Ventoux. It's long, but the gradients come nowhere near these climbs!

For such climbs, you'll want the lowest gearing you can possibly get. If your front rings are the stock compact 50/34 ones then the 38 rear you are considering is a good idea. 

But if you have the Shimano 105 5800 GS rear derailleur  (or similar), then you're out of luck, because 32 teeth is the most it can handle. 

So, you'll be needing either


a new rear derailleur, and / or front derailleur, or
borrow a bike with seriously low gears  (a carbon MTB with road tires would be good).


The next thing is training. Although you didn't ask here are my suggestions ... but firstly the good news ... hauling your body mass up a hill like Mont Ventoux means you have a serious level of strength and fitness. The key is to loose some of the mass while keeping the strength and endurance. 

From my observations for most males (it doesn't work the same for females) the best thing for weight loss is a 40 minute training ride before breakfast. To maintain strength, do hill repeats or efforts on gradients of 8 to 15% Find a steep and climb it once a month to track progress. Mix these rides with Long Slow Distance rides to maintain aerobic condition. Be careful not to overtrain; 3 rides per week is enough. 

I'm sure you don't need advice for the actual climbs, but for others who read this, such climbs should be started slowly, they get hard enough soon enough! 

Enjoy!