Lorentz invariance is considered as one of the fundamental symmetries in the laws of physics. However, many candidates of quantum gravity suggest the breaking of Lorentz invariance at the Planck energy scale. Numerous astrophysical observations and terrestrial experiments have been used to test the possibility of Lorentz-invariance violation with no positive evidence discovered. The successful detection of gravitational waves provides new hope for probing Lorentz-invariance violation. Together with the well-developed techniques in pulsar observation, we expect to set more stringent constraints on the violation of Lorentz invariance, in case no positive signatures are found in the era of multimessenger observational astronomy. In this talk, I will focus on the modifications to pulsar signals and continuous gravitational waves emitted by an isolated neutron star under Lorentz-violating gravity, showing the possibility of testing the fundamental symmetry using pulsar and continuous gravitational wave observations once eligible sources are detected.