"Every cloud has a silver lining " can be used in two ways, positive to cheer one up (for what it's worth), negative to just take an easy way out of someone's problem.
When something bad happens to someone it's easy to throw in: "Ach , well, every cloud etc."
"The lion's share", I don't know maybe to say it right, seems more like a matter of fact thing.

If this is definitely just a personal vieuw , then I'm glad to know.