  The exceptionally low-symmetry crystal structures of the time-reversal
symmetry breaking superconductors LaNiC$_2$ and LaNiGa$_2$ lead to an
internally-antisymmetric non-unitary triplet (INT) state as the only
possibility compatible with experiments. We argue that this state has a
distinct signature: a double-peak structure in the Density of States (DOS)
which resolves in the spin channel in a particular way. We construct a detailed
model of LaNiGa$_2$ capturing its electronic band structure and magnetic
properties ab initio. The pairing mechanism is described via a single
adjustable parameter. The latter is fixed by the critical temperature $T_c$
allowing parameter-free predictions. We compute the electronic specific heat
and find excellent agreement with experiment. The size of the ordered moment in
the superconducting state is compatible with zero-field muon spin relaxation
experiments and the predicted spin-resolved DOS suggests the spin-splitting is
within the reach of present experimental technology.
