From late 18th century to 1918 wies/village Rajskie (means PARADISELIKE) was predominantly a Lemko village w/its own Greek Catholic Church.The filial Roman Catholic Church was in Wolkowyja. Lisko was the POWIAT(county) and Baligrod was the GMINA (judicial/tax district).Historic Galicia Province, administered by ethnic Poles for the Austro-Hungarian Empire.Lemko emigrating in this time frame would have beenconsidered ethnically Rusniak/Rusyn, but Austrian citizen,During the Interwar Period (between WW1 & WW2) This region came under Reconstituted Poland's domain.Technically Poland had not existed as a geopolitical entity for the previous 125+ yrs. Anyone emigrating in this time frame would have be coming from Poland and considered a Polish citizen.Post WW2 Eastern Galicia became a part of SSR Ukraine under direct Soviet domain and Western Galicia continued under Polish domain under indirect Soviet domain.Today your ancestral village is in SE POLAND.
PS> Likely reason that family history has family changing surname upon immigration merely meansthat the surname looked like ?????/????? and became Lodyn. It was transliterated/sounds like from Cyrillic Alphabet to Latin Alphabet, but the surname never really changed.