Not yet reviewed by Pith; the record is open.

Unified theories such as string theory and loop quantum gravity allow the Lorentz Invariance Violation (LIV) at the Planck Scale ($M_P \sim 10^{19}$ GeV). Using an effective field theory, this effect can be observed at low energies in terms of new interactions with a strength of $\sim 1/M_P$. These new interactions contain operators with LIV coefficients which can be CPT-violating or CPT-conserving. In this work, we study in detail how these LIV parameters modify the transition probabilities in the next-generation long-baseline experiments, DUNE and T2HK. We evaluate the sensitivities of these experiments in isolation and combination to constrain the off-diagonal CPT-violating ($a_{e\mu}$, $a_{e\tau}$, $a_{\mu\tau}$) and CPT-conserving ($c_{e\mu}$, $c_{e\tau}$, $c_{\mu\tau}$) LIV parameters. We derive approximate compact analytical expressions of $\nu_{\mu}\to\nu_e$ and $\nu_{\mu}\to\nu_\mu$ probabilities in the presence of these LIV parameters to explain our numerical results. We explore the possible correlations and degeneracies between these LIV parameters & 3$\nu$ parameters $\theta_{23}$ & $\delta_{\rm CP}$. We find that for non-maximal values of $\theta_{23}$, there exist degenerate solutions in its opposite octant for standalone DUNE and T2HK. These degeneracies disappear when we combine the data from DUNE and T2HK. In case of no-show, we place the expected bounds on these CPT-violating and CPT-conserving LIV parameters at 95% C.L. using the standalone DUNE, T2HK, and their combination. We observe that due to its access to a longer baseline and high-energy neutrinos, DUNE has a better reach in probing all these LIV parameters as compared to T2HK. Since the terms containing the CPT-conserving LIV parameters are proportional to neutrino energy in oscillation probabilities, T2HK is almost insensitive to the CPT-conserving LIV parameters because it mostly deals with sub-GeV neutrinos.