Biosorption is a very effective technique to eliminate the heavy metals present in the wastewater that utilize nongrowing biomass. The adsorption ability of the Periyakulam-2 (PKM-2) variety of Moringa Oleifera leaves (MOLs) to eliminate Pb(II) and Zn(II) ions from an aqueous solution was examined in this work. Fourier transform infrared (FTIR) spectroscopy, field-emission scanning electron microscopy, energy-dispersive X-ray (EDX) analysis, X-ray powder diffraction, and Brunauer-Emmett-Teller methods were used to characterize the PKM-2 variety of MOLs. The set of variables consists of the metal ion initial concentration, a dosage of the adsorbent, and pH were optimized with the help of the response surface methodology to get maximum metal removal efficiency of lead and zinc metals using the PKM-2 MOL biosorbent. A maximum Pb(II) removal of 95.6% was obtained under the condition of initial concentration of metal ions 38 mg/L, a dosage of the adsorbent 1.5 g, and pH 4.7, and a maximum zinc removal of 89.35% was obtained under the condition of initial concentration of metal ions 70 mg/L, a dosage of the adsorbent 0.6 g, and pH 3.2. The presence of lead and zinc ions on the biosorbent surface and the functional groups involved in the adsorption process were revealed using EDX and FTIR analysis, respectively. The adsorption data were evaluated by employing different isotherm and kinetic models. Among the isotherm models, Langmuir’s isotherm showed that the best fit and maximum adsorption capacities are 51.71 and 38.50 mg/g for lead and zinc, respectively. Kinetic studies showed accordance with the pseudo-second-order model to lead and zinc metal adsorption. Thermodynamic parameters confirmed (ΔG° < 0, ΔH° < 0, and ΔS° > 0) that the sorption mechanism is physisorption, exothermic, spontaneous, and favorable for adsorption. The results from this study show that the MOL of the PKM-2 type is a promising alternative for an ecofriendly, low-cost biosorbent that can effectively remove lead and zinc metals from aqueous solutions.