Hexagonally ordered mesoporous carbon was ozonized, and the oxidized carbonaceous material was modified with L-arginine. The ozonized and L-arginine-modified carbons were extensively characterized and tested as Pb(II) ion adsorbents, with optimization of Pb(II) solution pH, exposure time, Pb(II) ion concentration and the presence of concurrent ions. Pb(II) adsorption equilibrium was achieved within 5 min at optimal pH = 2.6 or 5.3 for the oxidized and L-arginine-modified carbonaceous materials, respectively. The adsorption kinetics of both investigated materials were best described by the pseudo-first-order model. The maximum adsorption capacity for Pb(II) ions was determined to be 16 mg g−1 (ozonized material) or 45 mg g−1 (L-arginine-modified material). The Langmuir model provided the best fit for the adsorption isotherm data. Fe(III) ions mostly hindered the Pb(II) adsorption (up to 60%) on the L-arginine-modified carbon material. L-arginine-modified carbon was used to enrich Pb(II) from simulated urban roof runoff and its determination using the slurry sampling high-resolution continuum-source graphite furnace atomic absorption spectrometry technique. The developed analytical procedure was characterized by a limit of quantification of 2.63 µg L−1, an enrichment factor of 50, and a recovery rate of 94.8%.