The optimization of prediction and update operators plays a prominent role in lifting-based image coding schemes. In this paper, we focus on learning the prediction and update models involved in a recent Fully Connected Neural Network (FCNN)-based lifting structure. While a straightforward approach consists in separately learning the different FCNN models by optimizing appropriate loss functions, jointly learning those models is a more challenging problem. To address this problem, we first consider a statistical model-based entropy loss function that yields a good approximation to the coding rate. Then, we develop a multi-scale optimization technique to learn all the FCNN models simultaneously. For this purpose, two loss functions defined across the different resolution levels of the proposed representation are investigated. While the first function combines standard prediction and update loss functions, the second one aims to obtain a good approximation to the rate-distortion criterion. Experimental results carried out on two standard image datasets, show the benefits of the proposed approaches in the context of lossy and lossless compression.