We address a lifetime maximization problem for a single-hop wireless sensor network where multiple sensors encode and communicate their measurements of a Gaussian random source to a Fusion Centre (FC). The FC is required to reconstruct the source within a prescribed distortion threshold. The lifetime optimization problem is formulated as a joint power, rate and timeslot (for TDMA) allocation problem under the constraints of the well known rate distortion constraints for the Gaussian CEO problem, the capacity constraints of the wireless links, the energy constraints of the sensor nodes and the strict delay constraint within which the encoded sensor data must arrive at the FC.We study the performances of TDMA and an interference limited non-orthogonal multiple access (NOMA) (with single user decoding) based protocols and compare them against the upper bound provided by the optimal lifetime performance where the capacity constraints are given by the Gaussian multiaccess capacity region. While the constrained non-linear optimization problems for the TDMA and the Gaussian multiaccess cases are convex, the NOMA case results in a non-linear nonconvex D.C. (difference of convex functions) programming problem. We provide a simple successive convex approximation based algorithm for the NOMA case that converges fast to a suboptimal lifetime performance that compares favourably against the upper bound provided by the Gaussian multiaccess case. Extensive numerical studies are presented for both static and slow fading wireless environments with full channel state information at the fusion centre.