The Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission is a new two-probe lunar mission derived from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission. On 13 February 2010, one of the two probes, ARTEMIS P1 (formerly THEMIS-B), made the first lunar wake flyby of the mission. We present detailed analysis of the electrostatic waves observed on the outbound side of the flyby that were associated with electron beams. Halekas et al. (2011) derived a net potential across the lunar wake from observations and suggested that the net potential generated the observed electron beams and the electron beams in turn excited the observed electrostatic waves due to kinetic instabilities. The wavelengths and velocities of the electrostatic waves are estimated, using high-resolution electric field instrument data with cross-spectrum analysis and cross-correlation analysis. In general, the estimated wavelengths vary from a few hundred meters to a couple of thousand meters. The estimated phase velocities are on the order of 1000 km s(-1). In addition, we perform 1-D Vlasov simulations to help identify the mode of the observed electrostatic waves. We conclude that the observed electrostatic waves are likely on the electron beam mode branch.