We report on the experimental realization of a current-controllable lateral S-(S/F)-S Josephson junction based on the inverse proximity effect in the superconductor-ferromagnet bilayer (S/F). The dependence of the critical current on the magnetic field I c(B) shows a Fresenel-like pattern, which could qualitatively be understood with the theory of Josephson junctions in a magnetic field gradient. The amplitude and the period of the I c(B) pattern can be controlled by spin-polarized quasiparticles injection into the weak link. The period change suggests controllability of effective area of the Josephson junction. Furthermore, a temperature-induced transition from a weak-link behavior to a strong coupling between the superconducting banks is also observed in these lateral Josephson junctions.