  The effects of 2.5 MeV electron irradiation were studied in the
superconducting phase of single crystals of LaNiGa$_2$, using measurements of
electrical transport and radio-frequency magnetic susceptibility. The London
penetration depth is found to vary exponentially with temperature, suggesting a
fully gapped Fermi surface. The inferred superfluid density is close to that of
a single-gap weak-coupling isotropic $s-$wave superconductor. Superconductivity
is extremely robust against nonmagnetic point-like disorder induced by electron
irradiation. Our results place strong constraints on the previously proposed
triplet pairing state by requiring fine-tuned impurity scattering amplitudes
and are most naturally explained by a sign-preserving, weak-coupling, and
approximately momentum independent singlet superconducting state in LaNiGa$_2$,
which does not break time-reversal symmetry. We discuss how our findings could
be reconciled with previous measurements indicating magnetic moments in the
superconducting phase.
