In this article the design framework for an Adaptive Inverse Lattice Controller(AILC) with learning attributes, applicable to linear Auto Regressive (AR) systems, is presented. The utilized controller structure relies on the principle of Inverse Model Control (IMC) and its topology resembles that of a lattice filter. The adaptation rules depend on the identified system dynamics through an adaptive lattice filter. The identification scheme is extended with a proposed algorithm for the model order selection. Within the employed IMC-structure, an inverse lattice controller is utilized in the forward path in cascade with a lowpass detuning filter. As time progresses, the lattice filter estimates more accurately the system dynamics, and the learning scheme adjusts accordingly the attributes of the detuning filter. Simulation studies are used to investigate the efficacy of the suggested scheme.