  Superconductivity in noncentrosymmetric LaNiC$_2$ is expected to be induced
by electron--phonon interactions due to its lack of magnetic instabilities. The
non-Bardeen-Cooper-Schrieffer (BCS) behaviors found in this material call into
question the long-standing idea that relates unconventional superconductivity
with magnetic interactions. Here we report magnetic penetration-depth
measurements in a high-purity single crystal of LaNiC$_2$ at pressures up to
2.5 GPa and temperatures down to 0.04 K. At ambient pressure and below 0.5$T_c$
the penetration depth goes as $T^4$ for the in-plane and $T^2$ for the
out-of-plane component, firmly implying the existence of point nodes in the
energy gap and the unconventional character of this superconductor. The present
study also provides first evidence of magnetism in LaNiC$_2$ by unraveling a
pressure-induced antiferromagnetic phase inside the superconducting state at
temperatures below 0.5 K, with a quantum critical point around ambient
pressure. The results presented here maintain a solid base for the notion that
unconventional superconductivity only arises near magnetic order or
fluctuations.
