epsilon Lupi A is a binary system consisting of two main-sequence early B-type stars Aa and Ab in a short period, moderately eccentric orbit. The close binary pair is the only doubly magnetic massive binary currently known. Using photometric data from the BRITE Constellation we identify a modest heartbeat variation. Combining the photometry with radial velocities of both components we determine a full orbital solution including empirical masses and radii. These results are compared with stellar evolution models as well as interferometry and the differences discussed. We also find additional photometric variability at several frequencies, finding it unlikely these frequencies can be caused by tidally excited oscillations. We do, however, determine that these signals are consistent with gravity mode pulsations typical for slowly pulsating B stars. Finally we discuss how the evolution of this system will be affected by magnetism, determining that tidal interactions will still be dominant.