  Recent observations of galaxy clusters with the SCUBA instrument on the James
Clarke Maxwell Telescope have revealed a sample of gravitationally lensed
sources at sub-mm wavelengths. We extend our previous calculation on the
expected number of lensed optical arcs and radio sources to study the sub-mm
lensed source statistics due to foreground massive clusters. For a flat
cosmology with Omega_m=0.4 and Omega_Lambda =0.6, we predict roughly 1.5 \times
10^4 lensed sub-mm sources with flux densities greater than 4 mJy at 850
microns, and with amplifications due to lensing greater than 2, towards galaxy
clusters with X-ray luminosities greater than 8 x 10^44 h^-2 ergs s^-1 (0.3 to
3.5 keV band). We compare our predictions with observations from the SCUBA
instrument, and briefly consider the possibility of using the South Pole 10-m
sub-mm telescope and the Planck surveyor to identify lensed sub-mm sources. A
catalog of around 100 gravitationally lensed sources at 353 GHz may be a useful
by-product of Planck.
