  The Legendrian product of two Legendrian knots, as defined by Lambert-Cole,
is a Legendrian torus. We show that this Legendrian torus is a twist spun
whenever one of the Legendrian knot components is sufficiently large. We then
study examples of Legendrian products which are not Legendrian isotopic to
twist spuns. In order to do this, we prove a few structural results on the
bilinearised Legendrian contact homology and augmentation variety of a twist
spun. In addition, we show that the threefold Bohr-Sommerfeld covers of the
Clifford torus and Chekanov torus are not twist spuns.
