After asking about ten apartments, getting basically no replies and my friend in Lithuania also trying to call them, I finally got somewhere. I called my first Lithuanian phonecall! The broker didn't speak English, so I had to try to get by with my very limited skills. I didn't understand much, but asked if I could email him and he sent his email address and now I'm waiting for a reply. The apartment is still free and would be quite good, I think. At least based on the information online and the photos. But you never know...
But at the moment almost anything goes. I've got a week until the day I decided I'd go there, so I really need the apartment situation settled right now!
And after getting somewhere, the only answer I received was that the apartment has been rented to someone else. So I'm back to trying to get hold of people with apartments and still getting no answers...