Push Facebook Messages/ notifications / tweets vai Lithium API

nextuser the article you're referring to is for Lithium Social Web, not for the Lithium community.

In terms of community, if you want to post messages from the community to social network, I can think of two ways:

1- Add social media button to messages (this will be manual)

2- Use the Community API (v2 is probably best with the message resource) to pull the message you want, then post the message to the social network you want using their API (FaceBook API, Twitter API, LinkedIn API, ...)