Lorentz Invariance (LI) implies that the space-time structure is the same for all observers. On the other hand, various quantum gravity theories suggest that it may be violated when approaching the Planck scale. At extreme energies, like those available in the collision of Ultra-High En- ergy Cosmic Rays (UHECRs) with atmosphere nuclei, one should also expect a change in the interactions due to Lorentz Invariance Violation (LIV). In this work, the effects of LIV on the development of Extensive Air Showers (EAS) have been considered. After having introduced LIV as a perturbation term in the single-particle dispersion relation, a library of simulated showers with different energies, primary particles and LIV strengths has been produced. Possible LIV has been studied using the muon content of air showers measured at the Pierre Auger Observatory. Limits on LIV parameters have been derived from a comparison between the Monte Carlo expectations and muon fluctuation measurements from the Pierre Auger Observatory.