  The observed discrepancy of the Hubble parameter measurements in the local
universe with the cosmic microwave background (CMB) data may indicate a new
physics. It is vital to test the alternative models that reconcile the Hubble
tension with other cosmological observations in this direction. The CMB lensing
is a crucial observation that relates the early universe perturbations to the
matter's late-time distribution. In this work, we study the prediction of the
\"u$\Lambda$CDM as a solution for $H_0$ tension for CMB lensing and the low-
and high-$\ell$'s temperature (TT) power spectrum internal inconsistency. We
show that this model relaxes the low- and high-$\ell$'s TT mild inconsistency
and the CMB lensing tensions simultaneously. Accordingly, \"u$\Lambda$CDM
having the same number of free parameters as $\Lambda$CDM with lensing
amplitude $A_L$ added, has a better fit with $\Delta \chi^2=-3.3$.
