Drawing the Bernoulli lemniscate with level curves

I would like to draw the Bernoulli lemniscate (see below):

However, I would like to draw it in a similar way as the picture in the following question, which has already been answered: Relation between level curves and horizontal traces

In particular, I would like to highlight the level curve at the value 0, i.e. where f(x,y)=0 (for f the Bernoulli lemniscate).