Nice to meet you Emil. You probably got an answer to your question in the meantime: "where the Lenkey family comes from originally". Well if you did not then the fact is that the family origins fro Sajólenke (Nenke beforehand). This village is in the historic upper Gömör province, in historic Hungary.
Where are you from? For it would be quite foolish to correspond in English if we were both Hungarians.