Preprint by Griffin from Livermore Labs gives a theoretical explanation of LK-99's superconductivity and also explains why labs are having a hard time synthesizing it. There are two Pb sites in the crystal structure that Cu can substitute at, the lower energy one does nothing but it's the higher energy site that creates superconductivity.
https://arxiv.org/pdf/2307.16892.pdf
"Finally, the calculations presented here suggest that Cu substitution on the appropriate (Pb(1)) site displays many key characteristics for high-TC superconductivity, namely a particularly flat isolated d-manifold, and the potential presence of fluctuating magnetism, charge and phonons. However, substitution on the other Pb(2) does not appear to have such sought-after properties, despite being the lower-energy substitution site. This result hints to the synthesis challenge in obtaining Cu substituted on the appropriate site for obtaining a bulk superconducting sample."