  The possibility of Lorentz Invariance Violation (LIV) may appear in unified
theories, such as string theory, which allow the existence of a new space-time
structure at the Planck scale ($M_p \sim 10^{19}$ GeV). This effect can be
observed at low energies with a strength of $\sim 1/M_p$ using the perturbative
approach. In the minimal Standard Model extension (SME) framework, the neutrino
mass-induced flavor oscillation gets modified in the presence of LIV. The Iron
Calorimeter (ICAL) detector at the proposed India-based Neutrino Observatory
(INO) offers a unique window to probe these LIV parameters by observing
atmospheric neutrinos and antineutrinos separately over a wide range of
baselines in the multi-GeV energy range. In this paper, for the first time, we
study in detail how the CPT-violating LIV parameters $(a_{\mu\tau}, a_{e\mu},
a_{e\tau})$ can alter muon survival probabilities and expected $\mu^-$ and
$\mu^+$ event rates at ICAL. Using 500 kt$\cdot$yr exposure of ICAL, we place
stringent bounds on these CPT-violating LIV parameters at 95\% C.L., which are
slightly better than the present Super-Kamiokande limits. We demonstrate the
advantage of incorporating hadron energy information and charge identification
capability at ICAL while constraining these LIV parameters. Further, the impact
of the marginalization over the oscillation parameters and choice of true
values of $\sin^2\theta_{23}$ on LIV constraints is described. We also study
the impact of these LIV parameters on mass ordering determination and precision
measurement of atmospheric oscillation parameters.
