Within the lattice approach to loop quantum gravity on a fixed graph, explicit calculations tend to be involved and are rarely analytically manageable. However, being focused on a particularly interesting setting, concerned with expectation values with respect to coherent states on the lattice (sharply peaked on isotropic and flat cosmology), we are able to provide several simplifications which can facilitate approaching beyond-state-of-the-art problems. We present a step-by-step algorithm resulting in an analytical expression including up-to-first-order corrections in the spread of the coherent state. The algorithm is developed in such a way that it makes the computation straightforward and easily implementable.