A new class of truncation schemes of delta expansion on the lattice is studied. We show that the order of expansion in delta which is introduced as the dilation parameter can be taken as large enough and the result gives rise to the Borel transformation with respect to the relevant variable in the lattice models. The explicit simulation of the continuum scaling from the expansion effective at large spacings is investigated in anharmonic oscillators, the d = 2 nonlinear sigma model at large N and the Gross-Neveu model with Wilson fermions.