  In our previous study, we introduced a machine-learning technique, namely
CMBFSCNN, for the removal of foreground contamination in cosmic microwave
background (CMB) polarization data. This method was successfully employed on
actual observational data from the Planck mission. In this study, we extend our
investigation by considering the CMB lensing effect in simulated data and
utilizing the CMBFSCNN approach to recover the CMB lensing B-mode power
spectrum from multi-frequency observational maps. Our method is first applied
to simulated data with the performance of CMB-S4 experiment. We achieve
reliable recovery of the noisy CMB Q (or U) maps with a mean absolute
difference of $0.016\pm0.008\ \mu$K (or $0.021\pm0.002\ \mu$K) for the CMB-S4
experiment. To address the residual instrumental noise in the
foreground-cleaned map, we employ a "half-split maps" approach, where the
entire dataset is divided into two segments sharing the same sky signal but
having uncorrelated noise. Using cross-correlation techniques between two
recovered half-split maps, we effectively reduce instrumental noise effects at
the power spectrum level. As a result, we achieve precise recovery of the CMB
EE and lensing B-mode power spectra. Furthermore, we also extend our pipeline
to full-sky simulated data with the performance of LiteBIRD experiment. As
expected, various foregrounds are cleanly removed from the foreground
contamination observational maps, and recovered EE and lensing B-mode power
spectra exhibit excellent agreement with the true results. Finally, we discuss
the dependency of our method on the foreground models.
