  Discrete Weierstrass-type representations yield a construction method in
discrete differential geometry for certain classes of discrete surfaces. We
show that the known discrete Weierstrass-type representations of certain
surface classes can be viewed as applications of the $\Omega$-dual transform to
lightlike Gauss maps in Laguerre geometry. From this construction, further
Weierstrass-type representations arise. As an application of the techniques we
develop, we show that all discrete linear Weingarten surfaces of Bryant or
Bianchi type locally arise via Weierstrass-type representations from discrete
holomorhpic maps.
