Ok, so, Lubotin and jurisdictions.
The county was already Sáros ("muddy") in the 1400s, and while later rearrangements and regularizations doubtless moved a few boundaries, they did not affect Lubotin. The county seat was Eperjes (Prešov).
Hungarian counties were divided into administrative units called _járás_, which is literally "walking", so I like to translate it as "circuit", but it's more often termed "district". They were important in the day-to-day operations of government, but the boundaries and names changed too often for people to keep track, and they seldom affect archival recordkeeping. Lubotin was in the Felső Tárcza járás in all of the gazetteers that I checked.
But all this is only marginally relevant to vital records, because prior to the start of civil registration (Oct. 1, 1895), they were the responsibility of churches.
Ecclesiastic jurisdictions in Hungary basically consisted of local churches which reported to a bishop (or equivalent). If a village did not have a church of the right denomination for some of its residents, the relevant bishop assigned it to a nearby village that did. (Dvorzsák assembled his 1877 gazetteer with the primary purpose of identifying such assignments of recording location.)
Lubotin had a Roman Catholic church, and most of its residents were Roman Catholic. Greek Catholics were recorded in Pusztamező, and Jewish residents in Csircs. The relevant Roman Catholic bishopric was in Kassa (Košice), and the Greek Catholic one was in Eperjes. (Jewish administration was the exception; it did not really have any sort of central body.)
The gazetteers identify a few other details of administrativia. For example, in 1892 the courthouse was in Eperjes, the circuit judge and tax office were in Kisszeben (Sabinov), the train station was labeled "Lubotin-Lublófürdő", and the nearest telegraph office was in Orló.
The other detail in the gazetteers is the military assignments: draft district 67, home-guard regiment IX, militia circuit 29. (These can be relevant to tracking down information about WWI soldiers, but it all gets too confusing for me.)