Abstract: We examine the impact of Lorentz Invariance Violation (LIV) in measuring the octant of theta(23) and CP phases in the context of the Deep Underground Neutrino Experiment (DUNE). We consider the CPT-violating LIV parameters involving e-mu(a(e mu)) and e-tau (a(e tau)) flavors, which induce an additional interference term in neutrino and antineutrino appearance probabilities. This newinterference term depends on both the standard CP phase delta and the new dynamical CP phase phi(e mu)/phi(e tau), giving rise to new degeneracies among (theta(23), delta, phi). Taking one LIV parameter at-a-time and considering a small value of vertical bar a(e mu)vertical bar = vertical bar a(e tau)vertical bar = 5 x 10(-24) GeV, we find that the octant discovery potential of DUNE gets substantially deteriorated for unfavorable combinations of delta and phi(e mu)/phi(e tau). The octant of theta(23) can only be resolved at 3 sigma if the true value of sin(2) theta(23) less than or similar to 0.42 or >= 0.62 for any choices of delta and phi. Interestingly, we also observe that when both the LIV parameters a(e mu) and a(e tau) are present together, they cancel out the impact of each other to a significant extent, allowing DUNE to largely regain its octant resolution capability. We also reconstruct the CP phases delta and phi(e mu)/phi(e tau). The typical 1 sigma uncertainty on delta is 10-15 degrees. and the same on phi(e mu)/phi(e tau) is 25-30 degrees depending on the choices of their true values.