This paper is devoted to study the thermodynamics of charged de Sitter black holes in Einstein–Bumblebee gravity, a Lorentz-violating extension of general relativity, using an effective two-horizon framework that treats the region between the event and cosmological horizons as a single thermodynamic system. We derive globally consistent thermodynamic variables such as effective temperature, pressure, and volume and show that they satisfy a generalized first law. The effective heat capacity shows a strong Schottky-type anomaly, which is defined by a single-peak structure resulting from the interaction between the two horizons. It is demonstrated here that Lorentz-violating effects cause this feature to undergo systematic and controlled deformations. In particular, we observe that the Lorentz-violation parameter leads to a displacement and rescaling of the heat-capacity peak, which can be interpreted as a change of the effective excitation scale for the thermodynamic response. We also show that the overall thermodynamics of the two-horizon system can be effectively described by a phenomenological finite-level model, where the temperature difference between the horizons acts as an effective excitation gap. Although the map is not derived microscopically, it accurately reproduces the shape of the heat-capacity curve and allows one to interpret the macroscopic thermodynamical enhancement. Our results reveal that Lorentz-violating corrections act like a controlled change to the thermodynamics of black holes with multiple horizons. They keep the overall Schottky-type pattern but change the specific numerical details. This highlights the strong sensitivity of horizon thermodynamics to corrections beyond standard gravity and provides a systematic approach to study these deviations within a semiclassical framework.
Alessa et al. (Wed,) studied this question.