  Quasi-two-dimensional molecular conductor $\lambda$-(BETS)$_2$GaCl$_4$ shows
superconductivity (SC) below 5.5K, neighboring the dimer-type Mott insulating
phase. To elucidate the origin of SC and its gap function, we carry out
first-principles band calculation and derive a four-band tight-binding model
from the maximally localized Wannier orbitals. Considering the
spin-fluctuation-mediated mechanism by adding the Hubbard $U$-term to the
model, we analyze the SC gap function by applying the random phase
approximation. We show that the SC gap changes its sign four times along the
Fermi surface (FS) in the unfolded Brillouin zone, suggestive of a
$d$-wave-like SC gap, which only has two-fold symmetry because of the low
symmetry of the crystal structure. Decomposing the SC gap into the pairing
functions along the crystal axes, we compare the result to similar analysis of
the well-studied $\kappa$-type molecular conductors and to the experiments.
