There are a ton of examples that we could provide depending on your exact use-case (B2B community, B2C community, Support Community, Developer Community, Marketing Community, etc). However, maybe a good place to start would be this page:
From this page you can see not only a few of our flagship communities, but also the corresponding business stories that accompany a successful community.
FYI, this URL provides a 404 Error. Is there another resource to see other examples of communities built on Lithium? Thanks!