  A crucial step in the history of General Relativity was Einstein's adoption
of the principle of general covariance which demands a coordinate independent
formulation for our spacetime theories. General covariance helps us to
disentangle a theory's substantive content from its merely representational
artifacts. It is an indispensable tool for a modern understanding of spacetime
theories. Motivated by quantum gravity, one may wish to extend these notions to
quantum spacetime theories (whatever those are). Relatedly, one might want to
extend these notions to discrete spacetime theories (i.e., lattice theories).
This paper delivers such an extension with surprising consequences, extending
Part 1 (arXiv:2204.02276) to a Lorentzian setting.
  This discrete analog of general covariance reveals that lattice structure is
rather less like a fixed background structure and rather more like a coordinate
system, i.e., merely a representational artifact. This discrete analog is built
upon a rich analogy between the lattice structures appearing in our discrete
spacetime theories and the coordinate systems appearing in our continuum
spacetime theories. I argue that properly understood there are no such things
as lattice-fundamental theories, rather there are only lattice-representable
theories. It is well-noted by the causal set theory community that no theory on
a fixed spacetime lattice is Lorentz invariant, however as I will discuss this
is ultimately a problem of representational capacity, not of physics. There is
no need for the symmetries of our representational tools to latch onto the
symmetries of the thing being represented. Nothing prevents us from using
Cartesian coordinates to describe rotationally invariant states/dynamics. As
this paper shows, the same is true of lattices in a Lorentzian setting: nothing
prevents us from defining a perfectly Lorentzian lattice(-representable)
theory.
