The lemniscate $x^4-x^2+y^2=0$ was discussed in Gerono's Géométrie Analytique from 1854, see screenshot, while Lissajous's "Mémoire sur l'étude optique des mouvements vibratoires" is from 1857.
The book Le curve matematiche tra curiosità e divertimento notes that Cramer (1750) called the curve $(y+ax^2)^2=x^2-x^4$, a Quersackkurve, in latin bisaccium (a Quersack is a type of backpack).
The name lemniscate, from the Greek λημνίσκος = ribbon, was given to a different figure-8 curve, $(x^2+y^2)^2 + 2x^2 - 2y^2 = b$, by J. Bernoulli (1694). Yet another figure-8 curve, $ (x^2 + y^2)^2 = a x^2 + y^2$, was called hippopede = horse fetter by J. Booth. The history of that curve goes back to the ancient Greek mathematician Proclus (75 BC). See 2Dcurves.com
It is also stated that A. Aubry gave the $a=0$ curve the name lemniscate of Gerono in honor of his friend and colleague Camille Christophe Gerono. (I have not been able to locate Aubry's "Essai sur l'histoire de la géométrie des courbes".)
Huygens and Leibniz had corresponded on the curve $x^4-x^2+y^2=0$ in 1691, in an attempt to integrate the area enclosed by this curve. This predates both Gerono and Lissajous by one and half century...