There are nontrivial discrete subgroups of the Lorentz group. It is easy to construct an SO(3,1) matrix that has only integer entries and yet is not just a simple rotation. A rectangular lattice in Minkowski space is invariant under the group of these transformations. Different space-time lattices have different discrete subgroups of Lorentz under which they are invariant.
This might be what you are looking for, even if it does not answer the question ...
However, there is a snag: it is extremely difficult to construct any non-trivial dynamical model of nature (quantum, classical, anything) that transforms into itself under these discrete transformations, even if their lattice does. Versions of string theory, adapted to this lattice, may give you the best promises.
So my advice is: don't believe the no-go theorems.