I have setup a Gitlab strictly according to manual from the gitlab wiki. It works. I have a web access, I can create a project too (and git repo has been created after it).
Okay, I think I've got it.
When I add key for the user from web interface, it hasn't been added to authorized_keys file. What I do is make full delete of the gitolite installation and then reinstall it according to native manual from the gitolite wiki. Now when i've add a key to user, this key is added to authorized_keys and all works fine now.