Heavy metal pollution is posing a severe health risk on living organisms. Therefore, significant research efforts are focused on their detection. Here, we developed a sensing platform sensor for the selective detection of lead(II) acetate. The sensor is based on self-assembled polyethyleneimine-functionalized carbon nanotubes (PEI-CNTs) and graphene oxide films deposited onto gold interdigitated electrodes. The graphene-based nanostructure showed a resistive behavior, and the fabricated layer-by-layer film was used to detect Pb(II) acetate in an aqueous solution by comparison of three electrochemical methods: impedance spectroscopy, amperometry, and potentiometry stripping analysis. The results obtained from different methods show that the detection limit was down to 36 pmol/L and the sensitivity up to 4.3 μAL/μmol, with excellent repeatability. The detection mechanism was associated with the high affinity of heavy metal ions with the functional groups present in the PEI-CNTs and GO, allowing high performance and sensitivity. The achieved results are important for the research toward integrated monitoring and sensing platforms for Pb(II) contamination in drinking water.