  The heavy right-handed neutrinos in supersymmetric models can act as the
source of lepton flavor violation (LFV). LFV processes like $ \mu \rightarrow e
\gamma $, $ \tau \rightarrow \mu \gamma $, $ \tau \rightarrow e \gamma $ is an
effective way to explore new physics beyond the SM. Among the possible
processes, $ \mu $ decays have the greatest discovery potential in most of the
supersymmetric models. Experimental inference of lepton flavor-violating
processes within a supersymmetric type-II seesaw framework in the non-universal
Higgs model (NUHM) and non-universal Scalar Mass model for Yukawa mixing
scenarios in the $ S_{4} $ theory with an additional discrete symmetry is
presented. The numerical analysis includes full 2 loop renormalization group
running effects for the the above mentioned Yukawa coupling matrices. The
projected discovery reach of LFV experiments (MEG-II) is mentioned and those
regions in mSUGRA, NUHM, NUSM models that have already been excluded by the LHC
searches or that which is probed by MEG experiments is specified here. The
results presented in this work can influence experimental challenges and
physics motivations to construct various BSM theories and sensitivity to test
these theories at next run of HE/HL LHC is also considered.
