A method for lossless coding using a multi-resolution scheme with an adaptive lifting step is introduced. To this goal, a generalized lifting scheme, where the sums included in classical lifting are generalized to include possibly non linear and/or adaptive operations, is proposed. The conditions for the reversibility of the scheme are analyzed. Although the framework is valid for any type of sampled signals, we focus in particular on the discrete case (signals represented with a finite number of bits). Finally, experiments with a generalized prediction step are reported They show the interest of the approach for lossless compression.