  Inspired by recent experiments on graphene, we examine the non-dissipative
viscoelastic response of anisotropic two-dimensional quantum systems. We pay
particular attention to electron fluids with point group symmetries, and those
with discrete translational symmetry. We start by extending the Kubo formalism
for viscosity to systems with internal degrees of freedom and discrete
translational symmetry, highlighting the importance of properly considering the
role of internal angular momentum. We analyze the Hall components of the
viscoelastic response tensor in systems with discrete point group symmetry,
focusing on the hydrodynamic implications of the resulting forces. We show that
though there are generally six Hall viscosities, there are only three
independent contributions to the viscous force density in the bulk. To compute
these coefficients, we develop a framework to consistently write down the
long-wavelength stress tensor and viscosity for multi-component lattice
systems. We apply our formalism to lattice and continuum models, including a
lattice Chern insulator and anisotropic superfluid.
