  The precise measurements of Cosmic Microwave Background Anisotropy angular
power spectra made by the Planck satellite show an anomalous value for the
lensing amplitude, defined by the parameter $A_{lens}$, at more than $2$
standard deviations. 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 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 $\tau=0.055\pm0.010$ 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 will have the potential of
falsifying the current $A_{lens}$ anomaly at more than five standard deviation
and to strongly bound its frequency dependence. We also evaluate the future
constraints on a possible scale dependence for $A_{lens}$.
