A method and apparatus are disclosed for controlling the operation of an aftertreatment system for a motor vehicle having a Lean NOx Trap and a tail pipe for conveying exhaust gasses from the LNT to the external environment. Values are calculated for a NOx content in the exhaust gasses flowing in the tail pipe and the quantity of NOx stored in the LNT. A DeNOx request index is calculated as a function of these values. A raw threshold value of the DeNOx request index is calculated as a function of a LNT temperature and of an exhaust gas mass flow. A corrected threshold value of the DeNOx request index is calculated as a function of the raw threshold value of the DeNOx request index and of a correction factor. A DeNOx regeneration is initiated when the calculated value of the DeNOx request index is larger than the corrected threshold value.