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The magnetism in spin-orbit Mott insulators is closely related to the interplay between electronic correlations and spin-orbit couplings which often give rise to novel quantum phases of matter. In the Lacunar spinel GaTa₄Se₈, electronic correlations localize a single unpaired electron on tetrahedral clusters of Ta ions, while spin-orbit coupling generates J_eff=3/2 magnetic degrees of freedom. At T=50 K, GaTa₄Se₈ undergoes a magnetic transition accompanied by a structural dimerization. The magnetic ground states are entangled to the lattice distortion and a preceding phonon mode was observed by neutron scattering measurements. However, the mechanism of this preceding phonon mode is still unclear. In this presentation, I will present our crystallographic results following a series of neutron scattering measurements which provide more insights to the correlations between lattice and spin-orbital j_eff=3/2 states in cluster spin-orbit Mott insulator.