Lázár fought at the Siege of Buda (1686), where his father Miklós Apponyi died. He was personally raised to the hereditary rank of Baron by Charles VI in Vienna on 16 February 1718, for his outstanding military contribution to the Habsburg fights against the Ottoman Empire. Charles VI then made Lázár Count of Nagy-Appony on 30 May 1739 in Laxenburg, and his descendants kept that title until the end of the monarchic period. The family's coat of arms also dates from that moment.