In this paper, we designed a low turn-on voltage (VOn) AlGaN/GaN lateral field-effect rectifier (LFER) compatible with p-GaN gate high-electron-mobility transistor (HEMT) technology (PG-LFER). We also established an analytical model on the gated control two-dimensional-electron-gas density (nS) distributions and VOn to investigate the underlying mechanism. The designed PG-LFER features a p-GaN charge storage layer (CSL) under the anode terminal. Net negative charge density in the p-GaN CSL (sp-GaN) is associated with the activated doping concentration of p-GaN CSL (Np-GaN) and p-GaN CSL thickness (tp-GaN). VOn of the PG-LFER is significantly lowered due to the low sp-GaN caused by reducing the Np-GaN and tp-GaN. Meanwhile, the low VOn PG-LFER also preserves recognizable reverse blocking and capacitance characteristics. Verified by the calibrated simulation, the designed PG-LFER shows 70% lower VOn compared with the non-optimized LFER with a high sp-GaN. Compatible with p-GaN gate HEMT technology, the designed PG-LFER with improved performance is a promising candidate for power integrated applications.