We report a comprehensive investigation of the magnetic properties of LuFe2O4 (LFO) samples with different oxygen stoichiometries. Samples with excess oxygen exhibit spin glass behavior without long-range magnetic order, while three-dimensional ferrimagnetic order exists in a stoichiometric sample. Dissimilar experimental observations reported in several papers can be understood consistently when oxygen stoichiometry is taken into account. The stoichiometric sample orders magnetically below TN = 243 K, and a monoclinic lattice distortion sets in below TL = 175 K. This structural change is sensitive to the applied magnetic field, indicating strong spin-lattice coupling in this material. Unusual low-field thermal magnetization behavior was observed near TL, and its origin is discussed.