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Abstract We examine the impact of Lorentz Invariance Violation (LIV) in measuring the octant of $$\theta _{23}$$ θ23 and CP phases in the context of the Deep Underground Neutrino Experiment (DUNE). We consider the CPT-violating LIV parameters involving $$e - \mu $$ e-μ ($$a_{e\mu }$$ aeμ ) and $$e - \tau $$ e-τ ($$a_{e\tau }$$ aeτ ) flavors, which induce an additional interference term in neutrino and antineutrino appearance probabilities. This new interference term depends on both the standard CP phase $$\delta $$ δ and the new dynamical CP phase $$\varphi _{e\mu }$$ φeμ /$$\varphi _{e\tau }$$ φeτ , giving rise to new degeneracies among ($$\theta _{23}$$ θ23 , $$\delta $$ δ , $$\varphi $$ φ ). Taking one LIV parameter at-a-time and considering a small value of $$|a_{e\mu }| = |a_{e\tau }| = 5 \times 10^{-24}$$ |aeμ|=|aeτ|=5×10-24 GeV, we find that the octant discovery potential of DUNE gets substantially deteriorated for unfavorable combinations of $$\delta $$ δ and $$\varphi _{e\mu }$$ φeμ /$$\varphi _{e\tau }$$ φeτ . The octant of $$\theta _{23}$$ θ23 can only be resolved at $$3\sigma $$ 3σ if the true value of $$\sin ^2\theta _{23} \lesssim 0.42$$ sin2θ23≲0.42 or $$ > rsim 0.62$$ ≳0.62 for any choices of $$\delta $$ δ and $$\varphi $$ φ . Interestingly, we also observe that when both the LIV parameters $$a_{e\mu }$$ aeμ and $$a_{e\tau }$$ aeτ 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 $$\delta $$ δ and $$\varphi _{e\mu }$$ φeμ /$$\varphi _{e\tau }$$ φeτ . The typical $$1\sigma $$ 1σ uncertainty on $$\delta $$ δ is 10–15$$^{\circ }$$ ∘ and the same on $$\varphi _{e\mu }$$ φeμ /$$\varphi _{e\tau }$$ φeτ is 25–30$$^{\circ }$$ ∘ depending on the choices of their true values.