I’m trying to animate an object by applying a parametric equation to it, the Lissajous curve: https://en.wikipedia.org/wiki/Lissajous_curve
However, I could not find a way to do so in Blender. Is it possible to do so?
Welcome to BA 
It is possible to recreate any mathematical equation in Blender
The Wikipedia page you linked has a formula for X and Y, so assuming you want to move your object on the X and Y axises, just (in your item sidebar) go to the location XYZ, right click on X and Y, one at a time, and add a driver by using a #. You’ll then want to enter the equation. The T for time in your equation you can switch out with frame. The rest of the math… you can figure it out, it’s just multiplication and sin, and you can type in #sin(frame) to see that sin works great in Blender
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Thank you! Had no idea about drivers. Thanks for pointing that out, I’m going to dig around a little bit:
https://docs.blender.org/manual/en/latest/animation/drivers/usage.html#add-driver