Is there a way to make Lion's scrollbars visible on mouseover them?
I don't think there is a way to do either of your choices built in, and I don't know of any tool to do them for you. The only way to get this ability in every application would be to have a plugin which is automatically loaded into every application and replaces the default scrollbars. A possible workaround is to scroll just a little bit, so that the page doesn't move much. This will cause the scrollbars to become visible, and they won't hide again as long as either you are moving the mouse on top of that window, or you have the mouse above them. This means you can scroll a little, then move the mouse on top of them, and not worry about them disappearing.

If you want to try to implement this yourself you will probably need to create a custom NSScroller subclass, and find a way to make NSScrollView use it instead of the default class (I think NSScrollView has a private method to create a default scrollbar which you could override, but you will have to find it yourself).