It is now apparent that classical T Tauri-like outflows commonly accompany the formation of young brown dwarfs (BDs). To date two optical outflows have been discovered, and results presented in this Letter increase this number to three. Using spectro-astrometry, the origin of the LS-RCrA 1 forbidden emission lines in a blueshifted outflow is confirmed. The nondetection of the redshifted component of the outflow in forbidden lines, along with evidence for some separation between low- and high-velocity outflow components, does not support the hypothesis that LS-RCrA 1 has an edge-on accretion disk. The key result of this analysis is the discovery of an outflow component to the Hα line. The Hα line profile has blueshifted and redshifted features in the wings which spectro-astrometry reveals to also originate in the outflow. The discovery that Hα emission in BDs can have a significant contribution from an outflow suggests that the use of Hα line widths as a proxy of mass accretion in BDs is not clear cut. This method assumes that any contribution to the Hα line flux from a possible outflow is negligible. Finally, the fact that the Hα line traces both lobes of the outflow while only the blueshifted lobe is seen in forbidden emission points to the presence of a dust hole in the accretion disk of LS-RCrA 1. This is commonly seen in classical T Tauri stars and is assumed to signal the onset of planet formation.