  Polar lacunar spinels, such as GaV$_4$S$_8$ and GaV$_4$Se$_8$, were proposed
to host skyrmion phases under magnetic field. In this work, we put forward, as
a candidate for N\'eel-type skyrmion lattice, the isostructural GaMo$_4$S$_8$,
here systematically studied via both first-principles calculations and Monte
Carlo simulations of model Hamiltonian. Electric polarization, driven by
Jahn-Teller distortion, is predicted to arise in GaMo$_4$S$_8$, showing a
comparable size but an opposite sign with respect to that evaluated in V-based
counterparts and explained in terms of different electron counting arguments
and resulting distortions. Interestingly, a larger spin-orbit coupling of 4d
orbitals with respect to 3d orbitals in vanadium-spinels leads to stronger
Dzyaloshinskii-Moriya interactions, which are beneficial to stabilize a
cycloidal spin texture, as well as smaller-sized skyrmions (radius<10 nm).
Furthermore, the possibly large exchange anisotropy of GaMo4S8 may lead to a
ferroelectric-ferromagnetic ground state, as an alternative to the
ferroelectric-skyrmionic one, calling for further experimental verification.
