nils-drews
I wasn't sure if it was public or not ... You can add /status/version at the end of your community to get the version. Check this for full details.
Now, I believe a curl call should look like this one (couldn't try it unfortunately):
curl "https://eu.api.lithium.com/community/2.0/search?q=select * from messages&client_id=<your_client_id>&api.pretty_print=true"
You will need to get your client_id from the Lithium support. (And I think you need to create an 'application'. Works the same way as Google API)
This call, for the Lithium Bulk API (paid feature) worked fine:
curl "https://eu.api.lithium.com/lsi-data/v1/data/export/community/<community_id>?fromDate=201409010000&toDate=201409020000" -H "client-id:<my_client_id>" -u "<my_token_id>:"
Note: use api.lithium.com if your community is US based
Note2: I will provide more information as I learn more about the API v2 !