He was born in Paris, and was raised in a poor family who still managed to obtain a good education for their son.

He had courses with Antoine-René Mauduit at College Royale de France and Joseph-Francois Marie at Collége Mazaine of University of Paris.

In 1787 he began to teach at École Royale Militaire de Paris and he married Marie Nicole Sophie Arcambal.

"[1]: 140  In hindsight Ivor Grattan-Guinness observed:[1]: 183 The Traite is by far the most comprehensive work of its kind for that time.

The extent of its circulation is not known and it may not have been very large...But it is as well known as any other treatise of its time, and certainly more worth reading than any other, especially for the emerging generation.In 1799, he became professor of analysis at École Polytechnique.

When a second edition of the Traité du Calcul Différentiel et du Calcul Intégral was published in three volumes in 1810, 1814, and 1819, Lacroix renewed the text: New material, recording many of the advances made during the new century, were introduced throughout the text, which was rounded off by a long list of "Corrections and additions" and a splendid "Table of contents".

But the general impression is still that the main streams and directions of the calculus had been amplified and enriched, rather than changed in any substantial way.