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We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\Gamma$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$.

On the Variational Limits of Lattice Energies on Prestrained Elastic Bodies