Rb₂SO₄, Rb₂Ca₂(SO₄)₃, and Ba₃Lu(BO₃)₃ are structurally complex materials whose thermal expansion has been interpreted, on the basis of high-temperature x-ray diffraction, in terms of specific polyhedral rearrangements. We study their lattice dynamics and its consequences for thermal and electronic properties using molecular dynamics with actively learned moment tensor potentials trained on density-functional theory data. The anharmonicity measure σ^A (compares the anharmonic contribution to the interatomic forces with the total forces acting on atoms) reaches ≈0.3-0.5 for β-Rb₂SO₄, Rb₂Ca₂(SO₄)₃, and Ba₃Lu(BO₃)₃ and ≈0.75 for orientationally disordered α-Rb₂SO₄, and the imaginary harmonic modes of Rb₂Ca₂(SO₄)₃ and α-Rb₂SO₄ are stabilized at finite temperature. The simulations reproduce the measured thermal expansion and support the mechanisms proposed from diffraction: expansion along c in β-Rb₂SO₄ arises from both elongation and straightening of corrugated Rb chains, BO₃ reorientation accompanies the anisotropic expansion of Ba₃Lu(BO₃)₃, and bending of polyhedral linkages limits expansion along the weakly expanding directions and in cubic Rb₂Ca₂(SO₄)₃. Green-Kubo lattice thermal conductivities differ by more than an order of magnitude between compounds with comparable σ^A, showing that the anharmonicity measure alone does not determine heat transport. Phonon-induced band-gap renormalization, including lattice thermal expansion, reaches 2.7 and 1.7 eV at 1250 K in Rb₂Ca₂(SO₄)₃ and Ba₃Lu(BO₃)₃ and 1.4 eV at 650 K in β-Rb₂SO₄, with zero-point renormalizations of 0.64, 0.70, and 0.31 eV for β-Rb₂SO₄, Rb₂Ca₂(SO₄)₃, and Ba₃Lu(BO₃)₃, respectively.