According to David to Corot: French Drawings in the Fogg Art Museum by Agnes Mongan, pp. 207-208, this was done while Lucien was in Waterloo with his brother at the end of Napoléon's 100 day comeback tour between March to July of 1815. Lucien Bonaparte married twice, producing these offspring (from his article in thepeerage):
Children of Lucien Bonaparte and Catherine Christine Elenore Boyer —
Christine Charlotte Bonaparte (22 Feb 1795 - 6 May 1865)
unnamed son Bonaparte (13 Mar 1796 - 13 Mar 1796)
Victorie Gertrude Bonaparte (1797 - 1797)
Christine Charlotte Alexandrine Egypta Bonaparte (19 Oct 1798 - 19 May 1847)
Children of Lucien Bonaparte and Marie Laurence Charlotte Louise Alexandrine de Bleschamp —
Charles Lucien Jules Laurent Bonaparte, 2nd Prince de Canino et Musignano (24 May 1803 - 29 Jul 1857)
Laetitia Christine Bonaparte (1 Dec 1804 - 15 Mar 1871)
Joseph Lucien Bonaparte (14 Jun 1806 - 15 Aug 1807)
Jeanne Bonaparte (22 Jul 1807 - 22 Sep 1829)
Paul Marie Bonaparte (3 Nov 1808 - 5 Dec 1827)
Louis Lucien Bonaparte (4 Jan 1813 - 3 Nov 1891)
Pierre Napoléon Bonaparte (11 Oct 1815 - 7 Apr 1881)
Antoine Lucien Bonaparte (31 Oct 1816 - 28 Mar 1877)
Alexandrine Marie Bonaparte (10 Oct 1818 - 20 Aug 1874)
Constance Bonaparte (30 Jan 1823 - 5 Sep 1876)
According to David to Corot, the identities of the people has been discussed, but not settled.
From artist.maestro.fm-Lucien%20Bonaparte.html; a watermark in the lower right, below any of the figures, was removed with Photoshop.
Waistlines are high and skirts are narrow. The girls at the right wear high enclosing necklines, the girl furthest right wears a turtleneck. Alexandrine's dress has a high neckline and ruff. One girl's dress has a rounded neckline, the others square necklines. Mom's dress has mameluke sleeves, the girls to the right wear wide, but not puffed, sleeves while the girls to the left wear quarter length sleeves. A little girl to the left wears a midi-length skirt and pantaloons. Several girls have straight coiffures.
Keywords: 1815, Ingres, Alexandrine de Bleschamp, Princesse de Canino, Madame Juberthon, de Bleschamp family, Bonaparte family, Princess, turban, curly coiffure, straight coiffure, bun, high enclosing neckline, high neckline, ruff, scoop neckline, bertha, square neckline, epaulettes, quarter length full sleeves, long close sleeves, mameluke sleeves, cuffs, Empire waistline, necklace, earrings