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 T-N - 243K, and a monoclinic lattice distortion sets in below T-L - 175K. 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 T-L, and its origin is discussed. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4792036]