  Magnetic frustration is a route that can lead to the emergence of novel
ground states, including spin liquids and spin ices. Such frustration can be
introduced through either the geometry of lattice structures or by incompatible
exchange interactions. Identifying suitable strategies to control the degree of
magnetic frustration in real systems is an active field of research. In this
study, we devise a design principle for the tuning of frustrated magnetism on
the square lattice through the manipulation of nearest (NN) and next-nearest
neighbor (NNN) antiferromagnetic (AF) exchange interactions. By studying the
magnon excitations in epitaxially-strained La$_2$NiO$_4$ films using resonant
inelastic x-ray scattering (RIXS) we show that, in contrast to the cuprates,
the dispersion peaks at the AF zone boundary. This indicates the presence of an
AF-NNN spin interaction. Using first principles simulations and an effective
spin-model, we demonstrate the AF-NNN coupling to be a consequence of the
two-orbital nature of La$_2$NiO$_4$. Our results demonstrate that compressive
strain can enhance this coupling, providing a design principle for the
tunability of frustrated magnetism on a square lattice.
