Léon left the firm in 1872, and the firm was renamed J. Lévy & Cie. In 1895, when Lévy's two sons, Abraham Lucien Lévy and Gaspard Ernest Lévy, took over the firm, the company was renamed Lévy Fils et Cie. This firm became one of the most important postcard publishers in France.
About 1920, the firm was acquired by the printer émile Crété who also acquired the firm of Neurdein Frères, and the new combined company was known as Lévy et Neurdein Réunis. Throughout the various changes in the firm, the logo LL (registered as a trademark in 1901) continued to be used. In 1932, Lévy et Neurdein Réunis company was acquired by the Compagnie des Arts Photomécaniques (CAP).
The I.N.P. marque appears on some early view cards, and also the rear of some LL cards have the line "L'IMPRIMERIE NOUVELLE PHOTOGRAPHIQUE - PARIS". LL produced huge numbers of view cards of France and England. The firm also owned the following marks, at least by 1914: Fauvette, Mésange, . LL might have acquired Mésange at some stage, as the link occurs on the reverse of the later card shown here and not the former one. Revanche (see its own entry on this site) was also published or printed by the LL firm. The 1923 directory entry includes the marque EDIA for posters "artistique".
The shield which occurs to the address side of the card showing the Tartarin is that of the Union Syndicale maitres Imprimeurs de France.
This text incorporates some material from Dumbarton Oaks Research Library and Collection which I hope they will excuse in return for a link to their excellent site.