  We introduce a novel spinorial description for the higher-spin gauge theory
induced by the IKKT matrix model on an FLRW spacetime with Lorentzian
signature, called Lorentzian $\mathfrak{hs}$-IKKT theory. The new description
is based on Weyl spinors transforming under the space-like isometry subgroup
$SL(2,\mathbb{C})$ of the structure group $SO(2, 4) \simeq SU(2,2)$. It allows
us to exploit the full power of the spinor formalism in Lorentzian signature,
in contrast to a previous formalism based on the compact subgroup
$SU(2)_L\times SU(2)_R$ of $SU(2,2)$. Some cubic vertices of the Yang-Mills
sector and the corresponding scattering amplitudes are computed. We observe
that the $n$-point (for $n \geq 4$) tree-level amplitudes are typically
non-trivial on-shell, but exponentially suppressed in the late-time regime.
While Lorentz invariance of the higher-spin amplitudes is not manifest, it is
expected to be restored by higher-spin gauge invariance.
