A lignin-graft-(net-poly(acrylamide-co-N,N′methylenebisacrylamide)) copolymer was synthesized by conventional free-radical crosslinking copolymerization using conventional and microwave heating. Grafting of the polymer network onto lignin was confirmed by Fourier transform infrared spectroscopy (FTIR), nuclear magnetic resonance spectroscopy (NMR), scanning electron microscopy (SEM)/energy dispersive spectroscopy (EDS), thermogravimetric analysis (TGA), and elemental analysis. The performance of the modified materials for the removal of lead from water was evaluated. The materials obtained by the two types of heating showed excellent removal efficiencies: sample HLigAM4h, 96%; and sample HLigAMMW5, 86%. The maximum adsorption capacity of HLigAM4h was 209.82 mg g−1. The obtained copolymer (sample HLigAM4h) was characterized by X-ray photoelectron spectroscopy (XPS) and SEM/EDS after its evaluation as an adsorbent, which confirm the adsorption of Pb2+. This is the first of a series of studies on the topic, of a preliminary nature, with several other ones coming up in due time.