We have determined the lower critical magnetic field values of a single-crystal of type II superconductor LuNi2B2C at temperatures between 3K and 11K using cantilever magnetometry. This compound is part of a class of rare earth nickel borocarbides, whose properties are especially unusual in that they can simultaneously exhibit both superconductivity and magnetism, two competing states that were not previously known to coexist. The lower critical field values we obtained were much lower than expected. Our best guess is that the values for the lower critical field, Hc1, follow a quadratic dependence on temperature, although further research is needed to determine this to a high degree of certainty. This quadratic dependence indicates that there is some anisotropy between the single-crystal and polycrystalline forms of LuNi2B2C.