This work reports, for the first time, the analysis of tensor analyzing powers (T 20, T 21, T 22) along with the differential cross-section (CS) and the vector analyzing power iT 11 for the 6Li + 12C elastic scattering at 30 and 50 MeV within the framework of an optical model (OM) using microscopic shallow non-monotonic (NM) potentials. The NM potential is generated from the energy density functional formalism (EDF) (Brueckner et al (1968) Phys. Rev. 168 1184) using a realistic two-nucleon interaction incorporating the Pauli exclusion principle. The shallow NM potential can describe the experimental angular distributions of CS and analyzing powers of the elastic scattering data. The OM analysis of the data at 30 and 50 MeV does not indicate their sensitivity on the nuclear matter incompressibility K.