Laterally-coupled distributed feedback (LC-DFB) lasers use a lithographic fabrication step to define the distributed feedback grating, avoiding subsequent regrowth. Using higher order gratings can enhance the lithographic tolerance for lower resolution patterning, yielding lasers more amenable to fabrication. We show that LC-DFB lasers with higher order gratings, although requiring a higher threshold gain than those of first-order, provide a degree of longitudinal mode discrimination. Incorporating radiating partial waves, we have calculated modified coupled-mode coefficients for various duty cycles, grating orders, and grating geometries using a two-dimensional finite-element method. The modified coupled-mode equations were solved with and without a lambda/4 phase shift. The phase shift, while beneficial for first-order gratings, was found to generally diminish laser performance for lasers with higher order gratings.