  Timing of millisecond pulsars has long been used as an exquisitely precise
tool for testing the building blocks of general relativity, including the
strong equivalence principle and Lorentz symmetry. Observations of binary
systems involving at least one millisecond pulsar have been used to place
bounds on the parameters of Einstein-{\ae}ther theory, a gravitational theory
that violates Lorentz symmetry at low energies via a preferred and dynamical
time threading of the spacetime manifold. However, these studies did not cover
the region of parameter space that is still viable after the recent bounds on
the speed of gravitational waves from GW170817/GRB170817A. The restricted
coverage was due to limitations in the methods used to compute the pulsar
sensitivities, which parameterize violations of the strong-equivalence
principle in these systems. We extend here the calculation of pulsar
sensitivities to the parameter space of Einstein-{\ae}ther theory that remains
viable after GW170817/GRB170817A. We show that observations of the damping of
the period of quasi-circular binary pulsars and of the triple system PSR
J0337+1715 further constrain the viable parameter space by about an order of
magnitude over previous constraints.
