Nowadays, Ambient Backscatter Communication (AmBC) systems have emerged as a green communication technology to enable massive self-sustainable wireless networks by leveraging Radio Frequency (RF) Energy Harvesting (EH) capability. A Full-duplex Ambient Backscatter Communication (FAmBC) network with a Full-duplex Access Point (AP), a dedicated Legacy User (LU), and several Backscatter Devices (BDs) is considered in this study. The AP with two antennas transfers downlink Orthogonal Frequency Division Multiplexing (OFDM) information and energy to the dedicated LU and several BDs, respectively, while receiving uplink backscattered information from BDs at the same time. One of the key aims in AmBC networks is to ensure fairness among BDs. To address this, we propose the Multi-objective Lexicographical Optimization Problem (MLOP), which aims to maximize the minimum BD’s throughput while enhancing overall BDs’ throughput, subject to the AP’s subcarrier power, BDs’ reflection coefficients, and backscatter time allocation. Owe to the MLOP is non-convex, we propose Difference Convex Algorithm (DCA) using Exterior Penalty Function Method (EPFM)—an inventive non-convex optimization method— to reach the optimal solution. The most critical advantage of applying this proposed approach is finding the globally optimal solution. The effectiveness of the proposed method supported by theoretical analysis confirms its superiority compared to some of the investigated suboptimal algorithms with the same computational complexity.