  The Hall viscosity describes a non-dissipative response to strain in systems
with broken time-reversal symmetry. We develop a new method for computing the
Hall viscosity of lattice systems in strong magnetic fields based on momentum
transport, which we compare to the method of momentum polarization used by Tu
et al. [Phys. Rev. B 88 195412 (2013)] and Zaletel et al. [Phys. Rev. Lett. 110
236801 (2013)] for non-interacting systems. We compare the Hall viscosity of
square-lattice tight-binding models in magnetic field to the continuum integer
quantum Hall effect (IQHE) showing agreement when the magnetic length is much
larger than the lattice constant, but deviation as the magnetic field strength
increases. We also relate the Hall viscosity of relativistic electrons in
magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of
the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall
viscosity when the magnetic length is much larger than the lattice constant. We
also show that the Hall viscosity of the lattice model deviates further from
the continuum model if the $C_4$ symmetry of the square lattice is broken to
$C_2$, but the deviation is again minimized as the magnetic length increases.
