Lifting-based wavelet transform has been extensively used for efficient compression of various types of visual data. Generally, the performance of such coding schemes strongly depends on the lifting operators used, namely the prediction and update filters. Unlike conventional schemes based on linear filters, we propose, in this paper, to learn these operators by exploiting neural networks. More precisely, a classical Fully Connected Neural Network (FCNN) architecture is firstly employed to perform the prediction and update. Then, we propose to improve this FCNN-based Lifting Scheme (LS) in order to better take into account the input image to be encoded. Thus, a novel dynamical FCNN model is developed, making the learning process adaptive to the input image contents for which two adaptive learning techniques are proposed. While the first one resorts to an iterative algorithm where the computation of two kinds of variables is performed in an alternating manner, the second learning method aims to learn the model parameters directly through a reformulation of the loss function. Experimental results carried out on various test images show the benefits of the proposed approaches in the context of lossy and lossless image compression.