In this work, we propose a new technique of spatially-coupled low-density parity-check coding within a threshold-based lossy forwarding protocol for a multiple access relaying system. Here, block Rayleigh fading is assumed for all transmission links and error-free decoding at the relay is not required. Two schemes are presented in which the relay computes log-likelihood ratios (LLRs) of the network-coded symbols (from the sources) based on the received signals. By comparing the LLRs to a preset threshold, the relay decides to forward hard decisions when the network-coded symbol reliability is higher than the preset threshold. Otherwise, the relay decides to stay silent (first scheme) or to forward the LLRs to the destination (second scheme). Finally, we modify the LLR combining at the destination, based on an expression for the uncoded bit-error probability which is tailored to the proposed schemes. Simulation results demonstrate that the proposed relay protocol yields an improved bit-error rate performance compared to competitive schemes proposed in the literature.