We discuss the structural details and the ordering of hydrogen in LaHx for 2⩽x⩽3. To this end, we combine first-principles calculations with the cluster-expansion method. This approach allows us to follow the H occupation of the interstitial sites within the face-centered cubic matrix of La atoms. We find that LaHx clearly favors the fluorite structure at x=2 and adds excess H atoms at the octahedral interstitial sites. The ground-state behavior of the system is discussed and is found in agreement with experimentally observed structures at compositions LaH₂․₂₅ and LaH₂․₅; an additional ground state at composition LaH₂․₇₁ is predicted. The cluster expansion also permits an extensive scan of LaHx structures with two octahedral vacancies per unit cell. For energetically favorable configurations, this scan yields a vacancy percolation threshold at LaH₂․₇₅ that possibly drives the concentration-dependent metal-insulator transition: The band gap calculated for isolated vacancy pairs disappears for percolating vacancy chains. This transition from metallic to insulating state is also experimentally observed near to the composition LaH₂․₈ and gives rise to the “switchable mirror” phenomenon.