In this work, we investigated the sensing performance of epitaxial graphene on Si-face 4H-SiC (EG/SiC) for liquid-phase detection of heavy metals (e.g., Pb and Cd), showing fast and stable response and low detection limit. The sensing platform proposed includes 3D-printed microfluidic devices, which incorporate all features required to connect and execute lab-on-chip (LOC) functions. The obtained results indicate that EG exhibits excellent sensing activity towards Pb and Cd ions. Several concentrations of Pb2+ solutions, ranging from 125 nM to 500 µM, were analyzed showing Langmuir correlation between signal and Pb2+ concentrations, good stability, and reproducibility over time. Upon the simultaneous presence of both metals, sensor response is dominated by Pb2+ rather than Cd2+ ions. To explain the sensing mechanisms and difference in adsorption behavior of Pb2+ and Cd2+ ions on EG in water-based solutions, we performed van-der-Waals (vdW)-corrected density functional theory (DFT) calculations and non-covalent interaction (NCI) analysis, extended charge decomposition analysis (ECDA), and topological analysis. We demonstrated that Pb2+ and Cd2+ ions act as electron-acceptors, enhancing hole conductivity of EG, due to charge transfer from graphene to metal ions, and Pb2+ ions have preferential ability to binding with graphene over cadmium. Electrochemical measurements confirmed the conductometric results, which additionally indicate that EG is more sensitive to lead than to cadmium.