Lifting schemes have attracted much interest in different image processing tasks, and more specifically in the image compression field. In this context, the optimization of the lifting operators (i.e. the prediction and update ones) plays a crucial role in the design of efficient lifting-based image coding systems. In this respect, we propose in this paper to further investigate the exploitation of neural networks in a standard non-separable lifting scheme structure. More precisely, unlike previous works, where different neural network models are employed for all the prediction and update steps involved in a lifting scheme-based decomposition, our design consists in building a new multi-task convolutional neural network model that takes into account the similarities between two prediction stages. Simulations carried out on three popular image datasets show the benefits of the proposed learning-based image coding approach.