The objective of this paper is to investigate techniques for learning Fully Connected Network (FCN) models in a lifting based image coding scheme. More precisely, based on a 2D non separable lifting structure composed of three FCN-based prediction stages followed by an FCN-based update one, we first propose to resort to an p loss function, with p ∈ {1, 2}, to learn the three FCN prediction models. While the latter are separately learned in the first approach, a novel joint learning approach is then developed by minimizing a weighted p loss function related to the global prediction error. Experimental results, carried out on the standard Challenge Learned Image Compression (CLIC) dataset, show the benefits of the proposed techniques in terms of rate-distortion performance.