I will present an extension of the notion of general covariance to lattice theories. Just as we are able to write any continuum theory in any coordinate system we wish, we are also able to write any lattice theory using any lattice structure we wish. Moreover, just as we are able to write any continuum theory in a coordinate-free way, we are also able to write any embedded lattice theory in a lattice-structure-free way. This lattice-structure-free representation is spelled out in terms of bandlimited functions. The purpose of all of this reformulation and abstraction is that it clearly separates the substance of a theory from any superficial aspects which arise in a given coordinate/lattice representation. Ultimately this shows that the lattice structure underlying a ``lattice'' theory has the same level of physical import as coordinates do, i.e., none at all.
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