  Discrete linear Weingarten surfaces in space forms are characterized as
special discrete $\Omega$-nets, a discrete analogue of Demoulin's
$\Omega$-surfaces. It is shown that the Lie-geometric deformation of
$\Omega$-nets descends to a Lawson transformation for discrete linear
Weingarten surfaces, which coincides with the well-known Lawson correspondence
in the constant mean curvature case.

Differential Geometry