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The newly derived relativistic energy density functional [\textcolor{blue}{Phys. Rev. C \textbf{103}, 024305 (2021)}], which stems from the effectivefield theory motivated relativistic mean-field (E-RMF) is employed to establishthe appearance of peak/kink in the symmetry energy over the isotopic chain ofPb-nuclei. The coherent density fluctuation model parametrization procedure forfinite nuclei is adopted here to obtain the relativistic energy densityfunctional at local density. The relativistic energy density functional fromE-RMFT takes precedence over the Br\"uckner energy density functional as itaccurately predicts the empirical saturation density and binding energy pernucleon $E/A$, so-called 'Coester Band Problem'. Interestingly, using therelativistic energy density functional, it is possible to predict the peak at$N=126$ for recently developed G3 and widely used NL3 parameter sets, which isnot observed for Br\"uckener's functional in-spite of using the E-RMF density.From the present analysis, the newly fitted energy density functional is foundto be minutely sensitive to the choice of the parameter sets employed.

Appearance of peak in symmetry energy at N = 126 for Pb isotopic chain within relativistic energy density functional