Fundamental symmetry such as the Lorentz Invariance (LI) may spontaneously break at Planck scales in some unified theories. In a low energy effective field theory, such as the Standard Model, Violations of LI (VLI) can manifest itself perturbatively. Such Planck-suppressed VLI signals can affect the mass induced neutrino oscillations at accessible energy ranges and induce spectral changes by modifying both its magnitude and phase. High statistics neutrino experiments represent a potent source of information on neutrino oscillations stemming from its energy and direction dependent multi-layer matter effects. In this contribution, we present the physics reach of long baseline neutrino experiments, namely P2O and DUNE, in measuring sub-dominant effects in neutrino oscillations coming from possible VLI.