We explore the propagation of recently introduced optical coherence lattices (OCLs) in the turbulent atmosphere. We show that the lattice intensity profile and the spatial degree of coherence will display periodicity reciprocity over long propagation distances even though the lattices are affected by the turbulence. The lattice periodicity reciprocity has been previously conjectured to be advantageous for free-space information transfer and optical communications. We then show how one can increase the distance over which the lattice periodicity reciprocity is preserved in the turbulent atmosphere by engineering input lattice beam parameters. We also show that the OCLs have scintillation indices lower than those of Gaussian beams.