László was the son of Ferenc Thoroczkay de Toroczkószentgyörgy and Borbála Paczolay. The date and place of his birth have not been found.
His wife was Zsuzsanna Tholdalagi de Nagy-Iklód. They were married, but the date and place have not been found. Their seven known children were Klára (?-?), Péter (?-1680), Ferenc (?-?), Katalin (?-?), Borbála (?-?), Mátyás (?-?) and Mihály (?-?).
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