We consider the problem of joint rate scheduling and lossy data compression in a two-way relay network with distortion-sensitive stochastic packet traffic. A relay node facilitates exchanging packets between the two sources. Network coding at the relay improves energy efficiency at the expense of additional packet delay. In addition, network coding couples the source queues through the distortion levels of their individual packet traffic. This fact motivates having each source adapt the transmission rate and the compression ratio jointly. We first formulate a centralized dynamic scheme for scheduling and compression with the objective of minimizing the energy consumption at the relay while satisfying stability and average distortion constraints. Lyapunov stability arguments are used to define a centralized policy based on the instantaneous queue backlogs and distortion levels. In addition, a decentralized algorithm is proposed where sources have limited (1-bit) information about each other's queue backlog and distortion levels. Numerical results demonstrate that the performance of the proposed decentralized algorithm approaches the energy-delay tradeoffs resulting from the centralized solution.