It probably does, like a lot of widely used medication. But if it's not economical to extract lithium from batteries significantly made of it, it's certainly not economical to get it from waste water.

Fun fact: a big chunk of the lithium produced in the world is extracted from the Salar de Atacama: https://en.wikipedia.org/wiki/Salar_de_Atacama

The method is to concentrate the lithium (from <1% to 7%) via evaporation and then process this brine to produce lithium carbonate.