  Non-standard neutrino interactions (NSIs), the sub-leading effects in the
flavour transitions of neutrinos, play a crucial role in the determination of
the various unknowns in neutrino oscillations, such as neutrino mass hierarchy,
Dirac CP violating phase and the octant of atmospheric mixing angle. In this
work, we focus on the possible implications of lepton flavour violating (LFV)
NSIs, which generally affect the neutrino propagation, on the determination of
the these unknown oscillation parameters. We study the effect of these NSIs on
the physics potential of the currently running and upcoming long-baseline
experiments, i.e., T2K, NO$\nu$A and DUNE. We also check the allowed
oscillation parameter space in presence of LFV NSIs.
