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We examine the impact of Lorentz Invariance Violation (LIV) in measuring theoctant of $\theta_{23}$ and CP phases in the context of the Deep UndergroundNeutrino Experiment (DUNE). We consider the CPT-violating LIV parametersinvolving $e - \mu$ ($a_{e\mu}$) and $e - \tau$ ($a_{e\tau}$) flavors, whichinduce an additional interference term in neutrino and antineutrino appearanceprobabilities. This new interference term depends on both the standard CP phase$\delta$ and the new dynamical CP phase $\varphi_{e\mu}$/$\varphi_{e\tau}$,giving rise to new degeneracies among ($\theta_{23}$, $\delta$, $\varphi$).Taking one LIV parameter at-a-time and considering a small value of $|a_{e\mu}|= |a_{e\tau}| = 5 \times 10^{-24}$ GeV, we find that the octant discoverypotential of DUNE gets substantially deteriorated for unfavorable combinationsof $\delta$ and $\varphi_{e\mu}$/$\varphi_{e\tau}$. The octant of $\theta_{23}$can only be resolved at $3\sigma$ if the true value of $\sin^2\theta_{23}\lesssim 0.42$ or $\gtrsim 0.62$ for any choices of $\delta$ and $\varphi$.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 asignificant extent, allowing DUNE to largely regain its octant resolutioncapability. We also reconstruct the CP phases $\delta$ and$\varphi_{e\mu}$/$\varphi_{e\tau}$. The typical $1\sigma$ uncertainty on$\delta$ is $10^{\circ}$ to $15^{\circ}$ and the same on$\varphi_{e\mu}$/$\varphi_{e\tau}$ is $25^{\circ}$ to $30^{\circ}$ depending onthe choices of their true values.

Can Lorentz Invariance Violation affect the Sensitivity of Deep Underground Neutrino Experiment?