  We report the static and dynamic magnetic properties of LaSrCrO$_4$, a
seemingly canonical spin-3/2 square-lattice antiferromagnet that exhibits
frustration between magnetic layers -- owing to their AB stacking -- and offers
a rare testbed to investigate accidental-degeneracy lifting in magnetism.
Neutron diffraction experiments on single-crystal samples uncover a remarkable
anticollinear magnetic order below $T_N$ = 170 K characterized by a N\'eel
arrangement of the spins within each layer and an orthogonal arrangement
between adjacent layers. To understand the origin of this unusual magnetic
structure, we analyze the spin-wave excitation spectrum by means of inelastic
neutron scattering and bulk measurements. A spectral gap of 0.5 meV, along with
a spin-flop transition at 3.2\, T, reflect the energy scale associated with the
degeneracy-lifting. A minimal model to explain these observations requires both
a positive biquadratic interlayer exchange and dipolar interactions, both of
which are on the order of 10$^{-4}$ meV, only a few parts per million of the
dominant exchange interaction $J_1 \approx 11$ meV. These results provide
direct evidence for the selection of a non-collinear magnetic structure by the
combined effect of two distinct degeneracy lifting interactions.
