I haven't heard from such an integration. Does sound a bit like double the trouble.
You might want to use Lithium ActiveCast to include Litium content to other sites including your Joomla site: http://lithosphere.lithium.com/t5/Documentation-TKB/Admin-Guide-ActiveCast/ta-p/35880
As Claudius stated we don't officially integrate to Joomla's CMS platform, but the API does allow you to pull community capability into a dot com environment very easily. At it's simplest, you can use the Activecast modules in admin, which allow you to simply build a js type snippet of code to syndicate, say, the 5 latest solved questions from a forum. If you want to really go to town, you can use the REST API and build fully custom components that can access any part of the lithium platform allowing you to deeply integrate your dot com site and your community platform.
There is more info on the REST API in our Dev Nation section, which you have access to, plus if you're interested you can request a demo too.
Hope that helps.