  We study multidimensional quadrilateral lattices satisfying simultaneously
two integrable constraints: a quadratic constraint and the projective Moutard
constraint. When the lattice is two dimensional and the quadric under
consideration is the Moebius sphere one obtains, after the stereographic
projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by
an algebraic constraint imposed on the (complex) cross-ratio of the circular
lattice. We derive the analogous condition for our generalized isthermic
lattices using Steiner's projective structure of conics and we present basic
geometric constructions which encode integrability of the lattice. In
particular, we introduce the Darboux transformation of the generalized
isothermic lattice and we derive the corresponding Bianchi permutability
principle. Finally, we study two dimensional generalized isothermic lattices,
in particular geometry of their initial boundary value problem.
