  In the present work, we obtain the hydrostatic equilibrium configurations of
neutron stars in the recently proposed $f(R,\mathcal{L},T)$ theory of gravity,
for which $R$ is the Ricci scalar, $\mathcal{L}$ is the matter lagrangian
density, $T$ is the trace of the energy-momentum tensor and $f$ is a function
of the argument. This theory emerges in the present literature as a generalized
geometry-matter coupling theory of gravity. We derive the
Tolman-Oppenheimer-Volkoff-like equation for a particular functional form of
the $f(R,\mathcal{L},T)$ function. Our solutions are obtained from realistic
equations of state describing matter inside neutron stars. We obtain stable
solutions for neutron stars and we show that for some values of the free
parameter of the theory it is possible to be in agreement with both NICER and
LIGO/Virgo observational data.
