  Anisotropic lattice spacings are mandatory to reach the high temperatures
where chiral symmetry is restored in the strong coupling limit of lattice QCD.
Here, we propose a simple criterion for the nonperturbative renormalisation of
the anisotropy coupling in strongly-coupled SU($N$) or U($N$) lattice QCD with
massless staggered fermions. We then compute the renormalised anisotropy, and
the strong-coupling analogue of Karsch's coefficients (the running anisotropy),
for $N=3$. We achieve high precision by combining diagrammatic Monte Carlo and
multi-histogram reweighting techniques. We observe that the mean field
prediction in the continuous time limit captures the nonperturbative scaling,
but receives a large, previously neglected correction on the unit prefactor.
Using our nonperturbative prescription in place of the mean field result, we
observe large corrections of the same magnitude to the continuous time limit of
the static baryon mass, and of the location of the phase boundary associated
with chiral symmetry restoration. In particular, the phase boundary, evaluated
on different finite lattices, has a dramatically smaller dependence on the
lattice time extent. We also estimate, as a byproduct, the pion decay constant
and the chiral condensate of massless SU(3) QCD in the strong coupling limit at
zero temperature.
