  As the two phenomena, non-standard interaction (NSI) in neutrino propagation
and Lorentz invariance violation (LIV) modify the Hamiltonian of neutrino
oscillation in a similar fashion, it is very difficult to distinguish these two
effects. The only difference between them lies in the fact that NSI depends on
the matter density, whereas LIV is independent of the earth matter effect.
Therefore for a fixed baseline experiment, where matter density is constant,
the theories describing NSI and LIV are exactly equivalent. However, as the
present and future bounds of the NSI and LIV parameters are not equivalent, one
can distinguish these two scenarios in the long-baseline neutrino experiments
depending on their statistics with respect to the present and future bounds of
these parameters. In this paper, we attempt to differentiate between LIV and
NSI in the context of DUNE and P2SO, as these two future experiments are
believed to be sensitive to the strongest matter effect and will have very
large statistics. Taking LIV in the data and NSI in theory, our results show
that, indeed it is possible to have good discrimination between LIV and NSI.
The best separation between LIV and NSI at $3 \sigma$ C.L. is achieved for the
parameter $a_{\mu\mu}$ with P2SO. In this case, the value of LIV parameter for
which separation is possible, lies within its future bound, if one considers
the value of NSI parameter to be constrained by the present experiments.
Between DUNE and P2SO, the latter has better sensitivity for such
discrimination.
