We observed comet C/2007 N3 (Lulin) twice on UT 28 January 2009, using the UV grism of the Ultraviolet and Optical Telescope (UVOT) on board the Swift Gamma Ray Burst space observatory. Grism spectroscopy provides spatially resolved spectroscopy over large apertures for faint objects. We developed a novel methodology to analyze grism observations of comets, and applied a Haser comet model to extract production rates of OH, CS, NH, CN, C3, C2, and dust. The water production rates retrieved from two visits on this date were $6.7 ± 0.7$ and 7.9 $±$ 0.7 x 1E28 molecules s-1, respectively. Jets were sought (but not found) in the white-light and ‘OH’ images reported here, suggesting that the jets reported by Knight and Schleicher (2009) are unique to CN. Based on the abundances of its carbon-bearing species, comet Lulin is ‘typical’ (i.e., not ‘depleted’) in its composition.