This paper reports the synthesis of composite track-etched membranes (TeMs) modified with electrolessly deposited copper microtubules using copper deposition baths based on environmentally friendly and non-toxic reducing agents (ascorbic acid (Asc), glyoxylic acid (Gly), and dimethylamine borane (DMAB)), and comparative testing of their lead(II) ion removal capacity via batch adsorption experiments. The structure and composition of the composites were investigated by X-ray diffraction technique and scanning electron and atomic force microscopies. The optimal conditions for copper electroless plating were determined. The adsorption kinetics followed a pseudo-second-order kinetic model, which indicates that adsorption is controlled by the chemisorption process. A comparative study was conducted on the applicability of the Langmuir, Freundlich, and Dubinin–Radushkevich adsorption models to define the equilibrium isotherms and the isotherm constants for the prepared composite TeMs. Based on the regression coefficients R2, it has been shown that the Freundlich model better describes the experimental data of the composite TeMs on the adsorption of lead(II) ions.