The utilization of dredged sediment (DS) as a transformative material in building applications presents an ideal consumption strategy. This study endeavors to create a novel ceramsite lightweight aggregate (LWA) through the co-sintering of DS and rice husks (RHs), further integrating this LWA into the construction of pervious concrete. Results revealed that the optimum production procedure for the DS-based LWA incorporated a 21% RH addition, a sintering temperature of 1100 °C, and a sintering duration of 21 min. Notably, the optimal ceramsite LWA, denoted as SDC-H, exhibited a cylinder compressive strength of 28.02 MPa and an adsorption efficiency for Pb2+ of 94.33%. Comprehensive analysis (encompassing bulk density, cylinder compressive strength, water absorption, and the leaching concentrations of heavy metals) confirmed that SDC-H impacted the specification threshold of high-strength light aggregate derived from solid waste (T/CSTM 00548-2022). Substituting 50% of SDC-H led to a diminution in the mechanical properties but an improvement in the dynamic adsorption capacity of the innovative pervious concrete, registering a mechanical strength of 26.25 MPa and a cumulative adsorption capacity for Pb2+ of 285 mg/g. These performances of pervious concrete containing 50% SDC-H might correlate with the evolution of an interconnected and open-pore structure.