We have investigated the crystal structure and magnetic properties for polycrystalline samples of LaMn1-xFexO3+y, in the whole range x=0.0 to x=1.0, prepared by solid state reaction in air. All samples show the ORT-2 orthorhombic structure that suppresses the Jahn-Teller distortion, thus favoring a ferromagnetic (FM) superexchange (SE) interaction between Mn^{3+}-O-Mn^{3+}. For x=0.0 the oxygen excess (y ~ 0.09) produces vacancies in the La and Mn sites and generates a fraction around 18% of Mn^{4+} ions and 82% of the usual Mn^{3+} ions, with possible double exchange interaction between them. The Fe doping in this system is known to produce only stable Fe^{3+} ions. We find an evolution from a fairly strong FM phase with a Curie temperature T_{C} ~ 160 K, for x=0.0, to an antiferromagnetic (AFM) phase with T_{N} = 790 K, for x=1.0, accompanied by clear signatures of a cluster-glass behavior. For intermediate Fe contents a mixed-phase state occurs, with a gradual decrease (increase) of the FM (AFM) phase, accompanied by a systematic transition broadening for 0.2 < x < 0.7. A model based on the expected exchange interaction among the various magnetic-ion types, accounts very well for the saturation-magnetization dependence on Fe doping.