According to a footnote to the Quadrille in Grove’s Dictionary of Music and Musicians (1929 edition), the Quadrille des Lanciers was invented by Laborde in Paris in 1856 and is a quadrille with five figures for four couples in a square: Les Tiroirs, Les Lignes, Les Moulinets, Les Visites, and Les Lanciers. The date given there is certainly wrong, and the same edition of Grove’s has a more accurate article on the Lancers’ Quadrille, recognising that it was already a fashionable quadrille in 1850, was published in Dublin in 1817 [1] and was already popular in 1820 [2]. The Petit Journal ‘Album de Danses Illustrées’ claims English origins for the dance and notes that it was danced in Paris at the théâtre des Variétés in 1860. Revuz appears to accept this English (or Irish) origin and Sachs agrees [2].

1. https://www.regencydances.org/paper007.php [2/3/18]
2. C. Sachs, Eine Weltgeschichte des Tanzes (World History of the Dance, New York 1937)