Hi Anton,
While there was a way to use external live libraries by visiting the original file and enabling the library in one’s personal space, it seems that Figma removed that possibility without a warning a few days ago. Talking with support, I have found out that this type of sharing was mainly accidental.
I have created a feature request to ask for clarification on the matter, and for a supported way to share live libraries across spaces. Feel free to comment and upvote.
Thanks!