This paper investigates the quasinormal modes (QNMs) of a Lorentz-violating spacetime in the framework of Einstein-Bumblebee gravity, considering a cosmological constant. The study reveals that the interaction of spacetime with an anisotropic bumblebee field leads to distinct contributions to the axial and polar sectors of vector perturbations, breaking the isospectrality typically observed in vector modes. Numerical evidence indicates isospectral breaking in the vector modes of Einstein-Bumblebee black holes, with a pronounced break in the real part of the frequencies, while the imaginary component remains less affected. This isospectral breaking suggests the existence of two different waveforms in the Ringdown phase of the black hole, potentially offering a signal of quantum gravity observable in current experiments. The bumblebee field, when acquiring a nonzero vacuum expectation value, induces spontaneous Lorentz symmetry breaking, extending the standard general relativity formalism. The study explores the effects of Lorentz symmetry breaking on the spectral properties of vector modes in Einstein-Bumblebee black hole spacetimes. The paper presents numerical results using the matrix method and continued fraction method to calculate QNM frequencies, confirming the accuracy of the results through waveform fitting. The results show that the real part of the QNM frequencies initially increases and then decreases with the Lorentz violation parameter, while the imaginary part increases monotonically. The isospectral breaking is more pronounced with positive parameters and less so with larger azimuthal indices. The study also examines the dynamical evolution of vector fields during the ringdown phase, showing significant inconsistencies between axial and polar waveforms for non-zero Lorentz violation parameters. The results confirm that the nonzero vacuum expectation value of the bumblebee field leads to isospectral breaking of vector modes, attributed to the Lorentz violation parameter in the background metric. The findings suggest that isospectral breaking is foreseeable in modified gravity theories, with axial perturbations naturally decoupling from the bumblebee field, while polar perturbations show more complex behavior. The paper concludes that the isospectrality issue in gravitational perturbations is an interesting aspect within Einstein-Bumblebee gravity theory, with further research needed to understand the QNMs for polar modes in this theory.This paper investigates the quasinormal modes (QNMs) of a Lorentz-violating spacetime in the framework of Einstein-Bumblebee gravity, considering a cosmological constant. The study reveals that the interaction of spacetime with an anisotropic bumblebee field leads to distinct contributions to the axial and polar sectors of vector perturbations, breaking the isospectrality typically observed in vector modes. Numerical evidence indicates isospectral breaking in the vector modes of Einstein-Bumblebee black holes, with a pronounced break in the real part of the frequencies, while the imaginary component remains less affected. This isospectral breaking suggests the existence of two different waveforms in the Ringdown phase of the black hole, potentially offering a signal of quantum gravity observable in current experiments. The bumblebee field, when acquiring a nonzero vacuum expectation value, induces spontaneous Lorentz symmetry breaking, extending the standard general relativity formalism. The study explores the effects of Lorentz symmetry breaking on the spectral properties of vector modes in Einstein-Bumblebee black hole spacetimes. The paper presents numerical results using the matrix method and continued fraction method to calculate QNM frequencies, confirming the accuracy of the results through waveform fitting. The results show that the real part of the QNM frequencies initially increases and then decreases with the Lorentz violation parameter, while the imaginary part increases monotonically. The isospectral breaking is more pronounced with positive parameters and less so with larger azimuthal indices. The study also examines the dynamical evolution of vector fields during the ringdown phase, showing significant inconsistencies between axial and polar waveforms for non-zero Lorentz violation parameters. The results confirm that the nonzero vacuum expectation value of the bumblebee field leads to isospectral breaking of vector modes, attributed to the Lorentz violation parameter in the background metric. The findings suggest that isospectral breaking is foreseeable in modified gravity theories, with axial perturbations naturally decoupling from the bumblebee field, while polar perturbations show more complex behavior. The paper concludes that the isospectrality issue in gravitational perturbations is an interesting aspect within Einstein-Bumblebee gravity theory, with further research needed to understand the QNMs for polar modes in this theory.