One of the theories that has been taking shape in recent years, both in theoretical and experimental aspects, is the idea that Lorentz’s symmetry can be violated in the high energy regime, on the Planck scale. It seems that on this scale, the physics we know, based on the Standard Model and the Theory of Relativity, should be unified in a theory of quantum gravity. From this scenario, the possibility arises that the Lorentz symmetry, fundamental in Physics, may be broken on this scale of energy. Since the caliber symmetry breaking mechanism that occurs spontaneously and that explains, for example, mass creation in a boson theory, is known, it is possible that Lorentz symmetry can also be broken spontaneously . On the other hand, another phenomenon that generates discussions, but which is more accepted within the community is the possibility that particles that interact with a flutuating quantum field can perform a random movement similar to the observed by Robert Brown in the 19th century with pollen grains. This movement is sometimes called the quantum brownian motion (QBM). It has been shown that QBM can occur in a flat geometry or in a time dependent one. So, a good question to ask is what is the effect of Lorentz’s symmetry breaking for the quantum brownian motion performed by a point particle? in this work, we seek to answer these questions.