  We present a relativistic symmetry analysis of the allowed pairing states in
the noncentroymmetric superconductor LaNiC$_2$. The case of zero spin-orbit
coupling (SOC) is discussed first and then the evolution of the
symmetry-allowed superconducting instabilities as SOC is adiabatically turned
on is described. In addition to mixing singlet with triplet pairing, SOC splits
some triplet pairing states with degenerate order parameter spaces into
non-degenerate pairing states with different critical temperatures. We address
the breaking of time-reversal symmetry (TRS) detected in recent muon spin
relaxation experiments and show that it is only compatible with such
non-unitary triplet pairing states. In particular, an alternative scenario
featuring conventional singlet pairing with a small admixture of triplet
pairing is shown to be incompatible with the experimental data.
