You buy LaCl in the form of a fairly concentrated aqueous solution, generally a pool-care product like SeaKlear. You then dilute it with RO, and drip it into a stream of tank water passing through a very fine mechanical filter, such as a 5 micron sock.
It forms a precipitate (lanthanum phosphate, La04P) which is insoluble under normal reef tank conditions. It can remove extremely large quantities of phosphate very, very quickly and at a very low price. It can also bind with alkalinity, but with much lower affinity. That's generally only a consideration once you get to very low phosphate levels.
Downsides:
-More complicated to use than just plugging in a reactor, but then again cleaning a reactor isn't exactly all fun and games either.
-Need to source very fine mechanical filters.
-Need to observe tank to make sure the filter is catching the precipitate, and that alk is not being depleted.
-It will lower PO4 VERY quickly, which could be stressful to some corals.
If you've had such high levels for a long time, your rocks will likely continue to leach phosphate for a very long time to come, and unless you feel comfortable recharging it, I just can't really imagine GFO being an economical solution.
