  We investigate Nuclear Lattice Effective Field Theory for the two-body system
for several lattice spacings at lowest order in the pionless as well as in the
pionful theory. We discuss issues of regularizations and predictions for the
effective range expansion. In the pionless case, a simple Gaussian smearing
allows to demonstrate lattice spacing independence over a wide range of lattice
spacings. We show that regularization methods known from the continuum
formulation are necessary as well as feasible for the pionful approach.
