Lithium is a minor constituent, but its usual source is indeed salt, from the Dead Sea, Bolivian salars, and so on. Some rivers contain a better proportion of lithium.
Out of memory, brine is reacted with CO2 under pressure because essentially lithium precipitates then as carbonate. I guess lithium carbonate is then roasted to the oxide.
You can try ion exchange, but the carbonate process looks cheap. Or use ion exchange later, on the already concentrated lithium ions?