Wavelet decompositions based on lifting schemes have been widely used in image coding. Generally, the efficiency of such compression methods strongly depends on the design of the lifting operators, namely the prediction and update filters. To improve their performance, we propose in this paper to optimize these filters by resorting to two learning strategies. In the first one, classical Fully Connected Networks (FCNs) are exploited to perform the prediction and update. In the second approach, we develop an adaptive learning method that takes into account the input image, yielding a dynamical model of FCN. Experimental results, carried out on the standard Challenge Learned Image Compression (CLIC) dataset, show the benefits that can be drawn from the proposed approaches compared to conventional ones.