It is possible to create an implementation based on the above that decodes 24 dimensional points to the closest Leech lattice vector in < 1 microsecond per point on my AMD Ryzen laptop. Combine with some fast random projections/Johnson Lindenstrauss as described in the article to form the LSH.
This LSH family is unfortunately not present in FALCONN, but the alternatives in FALCONN are pretty good.