Jahn-Teller distortion and spin-phonon coupling in the lacunar spinel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>GaM</mml:mi> <mml:msub> <mml:mi mathvariant="normal">o</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <mml:msu

Lacunar spinels $\mathrm{A}{\mathrm{M}}_{4}{\mathrm{X}}_{8}$ ($\mathrm{A}=\mathrm{Ga}$, Ge, Al; $\mathrm{M}=\mathrm{V}$, Mo, Nb, Ta; $\mathrm{X}=\mathrm{S}$, Se) have garnered significant attention due to their remarkable properties, including multiferroicity, Mott-Hubbard gaps, and skyrmion phases. In this study, we present temperature-dependent Raman spectroscopy measurements of $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$, spanning the Jahn-Teller (JT) distortion and spin ordering transitions. Using group theory analysis and first-principles calculations, we identified and assigned ten Raman-active modes, among which the two lowest-energy modes, ${A}_{1}^{1}\phantom{\rule{4pt}{0ex}}({T}_{2}^{1})$ and ${A}_{1}^{2}\phantom{\rule{4pt}{0ex}}({T}_{2}^{2})$, were confirmed as JT active modes. The ${A}_{1}^{2}\phantom{\rule{4pt}{0ex}}({T}_{2}^{2})$ mode exhibits a redshift as the temperature approaches 50 K from both sides, indicative of a soft mode and suggesting a displacive nature for the ferroelectric transition. Additionally, anomalies observed in the ${A}_{1}$ and $E$ modes near 50 K and 25 K correlate with the JT transition and subsequent magnetic ordering, pointing to significant electron-phonon and spin-phonon coupling in $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$. These findings deepen our understanding of the mechanisms of the phase transition and the orbital-spin-lattice interactions in $\mathrm{GaM}{\mathrm{o}}_{4}{\mathrm{S}}_{8}$, while highlighting the crucial role of phonon dynamics in the $\mathrm{A}{\mathrm{M}}_{4}{\mathrm{X}}_{8}$ family.