We present detailed numerical modeling to predict expected X-ray signatures from lightning-induced electron precipitation (LEP) events. Simulations include the transionospheric propagation of the lightning electromagnetic pulse; ray tracing through the magnetosphere, including Landau damping; wave-particle interactions resulting in loss cone fluxes; and Monte Carlo simulation of the electron precipitation process, including bremsstrahlung photon production and propagation to a balloon observing platform. Modeling is included to show that our simulated events are consistent with subionospheric very low frequency observations of LEP. Simulations show that these events should be observable from balloon-based platforms. The modeled LEP event signatures, including X-ray flux, spectrum, and pulse shape, are then compared with observations of energetic X-ray pulses from the Balloon Array for Radiation-belt Relativistic Electron Losses 1U balloon taken in January 2013 and are shown to be highly consistent with the observations. The pulses were observed near L = 4, while the balloon was off the coast of Antarctica at about 70 • S, 5-20 • W. Correlations with GOES imagery and global lightning data, together with analysis of the temporal and spectral signatures of these pulses, led to the initial suggestion that these events could be signatures of LEP. However, for only a fraction of these events could a causative lightning discharge be identified in global lightning data sets. This poor correlation may be partially attributed to causative strokes being missed by the global lightning networks; nonetheless, we discuss other possible explanations for these events.