Right, remove the salt and minerals. We don't need that much salt, so we'd have to build pyramids or something with it. We drink the water, but then it ends up back in the oceans. The reason I mention that part is because if it didn't, if we could destroy the water, then the remaining water would retain the same salinity, and the concern would be that we drain the ocean dry, which is silly (I refer you back to how big it is). But we don't destroy water when we use it, so instead the worry is that we dilute all the world's ocean, which is also silly (I again refer you back to how big it is). We need a lot of batteries, but the sea is not useful as a source of lithium except as a byproduct. Even if it was the only source, the old batteries themselves would soon become a better source, as concentrated stores of lithium compared to the very-much-not-concentrated lithium in the ocean. But anyway the good places to mine lithium are on land (and are dried-up bits of ancient ocean, I think).
(I checked, some deposits are old lakebeds like https://en.wikipedia.org/wiki/Salar_de_Uyuni and others are igneous.)
It's also possible - true, I bet - that all the car batteries and storage batteries 8 billion people could possibly use are equivalent to only a tiny fraction of all the lithium in the ocean, but it would be harder arithmetic to confirm that, as well as being irrelevant on account of land-based mines existing.
Someone above said 4kg of magnesium per ton of seawater. Apparently lithium is 0.18g per ton of seawater.
That still means there's billions of tons of lithium in the seas, though.