  The nature of the pairing states of superconducting LaNiC$_2$ and LaNiGa$_2$
has to date remained a puzzling question. Broken time reversal symmetry has
been observed in both compounds and a group theoretical analysis implies a
non-unitary triplet pairing state. However all the allowed non-unitary triplet
states have nodal gap functions but most thermodynamic and NMR measurements
indicate fully gapped superconductivity in LaNiC$_2$. Here we probe the gap
symmetry of LaNiGa$_2$ by measuring the London penetration depth, specific heat
and upper critical field. These measurements demonstrate two-gap nodeless
superconductivity in LaNiGa$_2$, suggesting that this is a common feature of
both compounds. These results allow us to propose a novel triplet
superconducting state, where the pairing occurs between electrons of the same
spin, but on different orbitals. In this case the superconducting wavefunction
has a triplet spin component but isotropic even parity gap symmetry, yet the
overall wavefunction remains antisymmetric under particle exchange. This model
leads to a nodeless two-gap superconducting state which breaks time reversal
symmetry, and therefore accounts well for the seemingly contradictory
experimental results.
