  The Standard-Model Extension (SME) is an effective-field-theoretic framework
that catalogs all Lorentz-violating field operators. The anisotropic correction
from the minimal gravitational SME to Newtonian gravitational energy for
spheroids is studied, and the rotation of rigid spheroids is solved with
perturbation method and numerical approach. The well-known forced precession
solution given by Nordtvedt in the parameterized post-Newtonian formalism is
recovered and applied to two observed solitary millisecond pulsars to set
bounds on the coefficients for Lorentz violation in the SME framework. A
different solution, which describes the rotation of an otherwise
free-precessing star in the presence of Lorentz violation, is found, and its
consequences on pulsar signals and continuous gravitational waves (GWs) emitted
by neutron stars (NSs) are investigated. The study provides new possible tests
of Lorentz violation once free-precessing NSs are firmly identified in the
future.
