We compare the sensitivity of an interferometric measurement of gravity using a freely-falling, lasing atomic source to that achieved with a cold, thermal atomic source. We observe a higher fringe visibility with the lasing source, also the highest yet observed in such a configuration. We improve sensitivity by exploiting large momentum transfer beamsplitting (LMT), and discuss briefly the advantages of using a lasing atomic source for LMT. Most importantly, we measure no degradation of the sensitivity of our interferometer due to interaction induced dephasing at our limit of precision. Using a simple model, we verify this observation and project to beyond state-of-the-art sensitivities, concluding that with reasonable experimental parameters, interaction induced dephasing will not limit the sensitivity of inertial measurements using freely-falling, lasing atomic sources.