Could we say "sheds some important insights"?
E.g. The discussion sheds some important insights for optimizing an HTML parser
If this is not appropriate, what is a nice way to express the same idea?
I've never heard anyone use a phrase like that before. The idiom is "to shed some light on" not "to shed some insights for".
So you could say:
I think both of these convey the idea you're trying to express, although the second sentence states it a bit more directly.