Albert was the son of Miklós Lónyay de Nagylónya but his mother is unknown. The date and place of his birth have not been found.
His wife was Erzsébet Csapy. They were married, but the date and place have not been found. Their four known children were Kristóf (?-?), Péter (?-?), Farkas (?-?) and Mária (?-?).