The precise measurements of cosmic microwave background (CMB) anisotropy angular power spectra made by the Planck satellite show an anomalous value for the lensing amplitude, defined by the parameter A lens , at about 2 standard deviations (2.6 standard deviations when cosmic shear data are included). Moreover, considering A lens brings the values of the cosmological parameters determined by Planck in better agreement with those found by pre-Planck data sets. In this paper, after discussing the current status of the anomaly, we quantify the potential of future CMB measurements in confirming/falsifying the A lens tension. We find that a space-based experiment such as LiteBIRD could falsify the current A lens tension at the level of 5 standard deviations. Similar constraints can be achieved by a stage-III experiment assuming an external prior on the reionization optical depth of τ ¼ 0.055 AE 0.010 as already provided by the Planck satellite. A stage-IV experiment could further test the A lens tension at the level of 10 standard deviations. A comparison between temperature and polarization measurements made at different frequencies could further identify possible systematics responsible for A lens > 1. We show that, in the case of the CMB-S4 experiment, polarization data alone have the potential of falsifying the current A lens anomaly at more than 5 standard deviations and to strongly bound its frequency dependence. We also evaluate the future constraints on a possible scale dependence for A lens .