Lorentz Invariance Violation (LIV) represents a potential violation in Lorentz symmetry, a fundamental symmetry underlying all physical laws. Analyzing the effects of LIV on neutrino oscillation probabilities provides a promising avenue for evaluating potential violations of Lorentz invariance. Since the contribution of LIV is expected to be sub-dominant, it can be incorporated as a small perturbation to the standard matter Hamiltonian. The effective Hamiltonian for LIV can be studied using the Standard Model Extension (SME) framework. In our study, we implement this effective LIV Hamiltonian to numerically calculate the altered neutrino oscillation probabilities. We independently examine the effects of the LIV CPT-odd ( \(a_{\alpha \beta }\) ) and CPT-even ( \(c_{\alpha \beta }\) ) terms on neutrino oscillations, with the Deep Underground Neutrino Experiment (DUNE) serving as a case study for long-baseline experiments. Our analysis explores potential correlations among different LIV and standard oscillation parameters.