The hybrid trapped field magnet lens (HTFML), proposed by the authors in 2018, is a promising device that is able to concentrate a magnetic field higher than the applied field continuously, even after removing the external applied field. In this study, we have investigated the optimized performance of the HTFML consisting of a GdBaCuO magnetic lens and a hollow, cylindrical EuBaCuO trapped field magnet (TFM) for various applied fields, B_app, at 77 K using liquid nitrogen. A maximum concentrated magnetic field of B_c = 1.83 T was obtained experimentally in the central bore of the HTFML for B_app = 1.80 T. For B_app higher than 1.80 T, the B_c value decreased, and was lower than the trapped field, B_t, in the single EuBaCuO TFM cylinder from field cooled magnetization. We have individually analyzed the electromagnetic behavior of the HTFML, single TFM hollow cylinder, and single magnetic lens during the magnetizing process using experimental and numerical simulation results. When the B_c value in the HTFML is lower than the B_t value of the single TFM cylinder for an identical B_app, the magnetic lens in the HTFML becomes partially magnetized, resulting in the generation of a negative magnetic field in the opposite direction. As a result, the concentrated field in the HTFML is reduced after the magnetizing process. The optimum applied field, B_app, which is the same magnitude as the maximum trapped field ability of the single TFM cylinder, provides the best performance. The maximum B_c value, and the B_app value that results in this B_c value, are determined by the critical current density, J_c(B), characteristics of the bulk superconducting material used in the magnetic lens and TFM hollow cylinder in the HTFML.