In this letter, we propose an online power allocation (PA) method to maximize energy efficiency (EE) in energy harvesting systems with realistic battery constraints for two receivers. The optimization problem in this system configuration is challenging since it has a non-convex fractional form and the information of channel quality and the harvested energy can only be obtained causally in practice. To overcome these issues, we design time-average EE maximization through Lyapunov optimization techniques where the transmission power is computed with current battery information and channel fading. Moreover, based on random matrix theory, we present a simplified online EE algorithm. Numerical experiments verify that the proposed PA outperforms conventional online approaches with much reduced computational complexity.