  We study the prospects of detecting continuous gravitational waves (CGWs)
from spinning neutron stars (NSs), gravitationally lensed by the galactic
supermassive black hole. Assuming various astrophysically motivated spatial
distributions of galactic NSs, we find that CGW signals from a few ($\sim 0-6$)
neutron stars should be strongly lensed. Lensing will produce two copies of the
signal (with time delays of seconds to minutes) that will interfere with each
other. The relative motion of the NS with respect to the lensing optical axis
will change the interference pattern, which will help us to identify a lensed
signal. Accounting for the magnifications and time delays of the lensed
signals, we investigate their detectability by ground-based detectors.
Modelling the spin distribution of NSs based on that of known pulsars and
assuming an ellipticity of $\epsilon = 10^{-7}$, lensed CGWs are unlikely to be
detectable by LIGO and Virgo in realistic searches involving
$\mathcal{O}(10^{12})$ templates. However, third generation detectors have a
$\sim 2-51\%$ probability of detecting at least one lensed CGW signal. For an
ellipticity of $\epsilon = 10^{-8}$, the detection probability reduces to $\sim
0-18 \, \% $. Though rare, such an observation will enable interesting probes
of the supermassive black hole and its environment.
