My guess is that the presence of lithium in the groundwater is in trace amounts if at all, while the dosing of lithium is in the domain of ~300mg. A casual search for the quantity of lithium in brine from a mine shows a max of 1400ppm for a rich mine in Chile[1] so drinking straight brine wouldn't get you anywhere near the therapeutic dose. Good question!
[1]: https://www.sciencedirect.com/science/article/abs/pii/S01691...