The lemniscate $x^4-x^2+y^2=0$ was discussed in Gerono's <A HREF="https://archive.org/details/gomtrieanalytiq00gerogoog">Géométrie Analytique</A> from 1854, see screenshot, while Lissajous's "Mémoire sur l'étude optique des mouvements vibratoires" is from 1857.

<IMG SRC="https://ilorentz.org/beenakker/MO/Gerono.png"/>

The book <A HREF="https://books.google.nl/books?id=CWazJtSI2L0C&pg=PA172&lpg=PA172">Le curve matematiche tra curiosità e divertimento</A> notes that Cramer (1750) called the curve $(y+ax^2)^2=x^2-x^4$, a *Quersackkurve*, in latin *bisaccium* (a <A HREF="https://de.wikipedia.org/wiki/Quersack">Quersack</A> is a type of backpack).    
<sub>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 <A HREF="http://www.2dcurves.com">2Dcurves.com</A></sub>

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".)

Concerning issues of priority, Huygens and Leibniz had <A HREF="https://books.google.nl/books?id=lIZ0v23iqRgC&pg=PA306">corresponded</A> on the curve $x^4-x^2+y^2=0$ in 1691, in an attempt to integrate the area enclosed by this self intersecting curve. (A quadrature which Newton had claimed to be impossible.) This predates both Gerono and Lissajous by one and half century...