  We study effects of Lorentz-invariance violation on the rotation of neutron
stars (NSs) in the minimal gravitational Standard-Model Extension framework,
and calculate the quadrupole radiation generated by them. Aiming at testing
Lorentz invariance with observations of continuous gravitational waves (GWs)
from rotating NSs in the future, we compare the GW spectra of a rotating
ellipsoidal NS under Lorentz-violating gravity with those of a
Lorentz-invariant one. The former are found to possess frequency components
higher than the second harmonic, which does not happen for the latter,
indicating those higher frequency components to be potential signatures of
Lorentz violation in continuous GW spectra of rotating NSs.
