He won the mathematics section prize of the Berlin Academy of Sciences for 1784 in response to a question on the foundations of the calculus. The work was published in his 1787 book Exposition elementaire des principes des calculs superieurs. (A Latin version was published in 1795.) Although L'Huilier won the prize, Joseph Lagrange, who had suggested the question and was the lead judge of the submissions, was disappointed in the work, considering it "the best of a bad lot." Lagrange would go on to publish his own work on foundations, and Augustin Louis Cauchy would later create the definitive approach.
Note that this surname is sometimes rendered as Lhuilier or Lhuillier.