A lining is an inside layer of material found on curtains and in coats and jackets.
As a metaphor, this idiom means that out of every bad situation or event, something good comes. So, it's a rather positve and optimistic perspective.
Of course, for some people, real clouds are full of silvery joy and none more so, than stormchasers; people who love to watch and even be inside the extreme weather conditions and tornados often found in the mid-west of America - like this.
Hold onto your hat!