  We present measurements of polarization lensing using the 150 GHz maps which
include all data taken by the BICEP2 & Keck Array CMB polarization experiments
up to and including the 2014 observing season (BK14). Despite their modest
angular resolution ($\sim 0.5^\circ$), the excellent sensitivity ($\sim
3\mu$K-arcmin) of these maps makes it possible to directly reconstruct the
lensing potential using only information at larger angular scales ($\ell\leq
700$). From the auto-spectrum of the reconstructed potential we measure an
amplitude of the spectrum to be $A^{\phi\phi}_{\rm L}=1.15\pm 0.36$ (Planck
$\Lambda$CDM prediction corresponds to $A^{\phi\phi}_{\rm L}=1$), and reject
the no-lensing hypothesis at 5.8$\sigma$, which is the highest significance
achieved to date using an EB lensing estimator. Taking the cross-spectrum of
the reconstructed potential with the Planck 2015 lensing map yields
$A^{\phi\phi}_{\rm L}=1.13\pm 0.20$. These direct measurements of
$A^{\phi\phi}_{\rm L}$ are consistent with the $\Lambda$CDM cosmology, and with
that derived from the previously reported BK14 B-mode auto-spectrum ($A^{\rm
BB}_{\rm L}=1.20\pm 0.17$). We perform a series of null tests and consistency
checks to show that these results are robust against systematics and are
insensitive to analysis choices. These results unambiguously demonstrate that
the B-modes previously reported by BICEP / Keck at intermediate angular scales
($150\lesssim\ell\lesssim 350$) are dominated by gravitational lensing. The
good agreement between the lensing amplitudes obtained from the lensing
reconstruction and B-mode spectrum starts to place constraints on any
alternative cosmological sources of B-modes at these angular scales.
