Quantum low-density parity-check (QLDPC) codes with asymptotically nonzero rates are promising candidates for fault-tolerant quantum computation. Belief propagation (BP) based iterative decoding algorithms, a primary choice for classical LDPC codes, perform poorly for QLDPC codes due to stabilizer-induced trapping sets, resulting in a high error floor. Several decoding algorithms, like post-processing decoders, normalized BP decoders, and neural decoders, have been proposed to increase the performance in the error-floor region. However, this improvement comes at the expense of an increase in the execution time of the decoder. This paper proposes a general framework for error correction for a class of QLDPC codes called lifted-product codes using recurrent neural networks (RNNs). The RNN is employed to learn message-passing rules that can decode quantum-trapping sets. Then the standard message-passing rules are used with the learned rules to improve the error floor. While training the RNN, the quasi-cyclic property of the lifted product codes is exploited to reduce the size of the training set and the number of parameters in the network. This reduction in the number of parameters makes these decoders amenable to hardware implementation. Simulation results show that the proposed decoder performs better than the existing decoders in the literature.