score:2
It was not clear from the question if there actually was a self-drop counter for LH there (which in that case was out of service?) or not. Assuming there wasn't:
One likely cause is "Not willing to pay for being the pioneer" or otherwise not getting the payback. Although I suppose LH is big also there. If you are (among) the first self-drop counter(s) on a specific ariport/market, you end up paying for:
It is a lot nicer to sit and wait for the pioneer to invest, and you wait and automate only once the customers are used to it. Then it may become a game where everyone is just waiting. I don't know if this is the case in Dubrovnik, though.
LH has been early to "pay the price" (=good investment) introducing self-service at their main sites. I live in Japan, and here, I believe that the initially late introduction of similar systems is, yes, partly due to culture, but partly due to having oligopoly between 2 companies (ANA and JAL) and thus both waiting for the other one to start.
p.s. I hesitated writing this as an answer and not a comment, but there may anyway not be enough people who have researched enough onto this.