Once you have a mixed rare earth solution, you still do not have lanthanum oxide. You have a chemically similar lanthanide mixture that must be split into individual product streams.
Solvent extraction is the workhorse
Industrial rare earth separation is dominated by solvent extraction (SX) with long trains and careful control. Reviews describe SX circuits as complex and stage-intensive, and this is the step that concentrates both cost and know-how.
Lanthanum is on the "lighter end," so it is generally easier than tight heavy-REE splits, but it still competes for capacity, and plant scheduling can absolutely affect lanthanum output.
A very practical lanthanum problem: La vs Ce handling
In light rare earth circuits, cerium chemistry (including oxidation state control) often shapes how early separations are structured and how "lanthanum-rich" raffinate streams are generated. This is one reason La output is not just "turn the mine on." (Lanthanum is produced as part of the circuit logic.)
Translation: Lanthanum supply depends on how separation plants configure their circuits and what products they prioritize.