  We study the one loop correction to the closed bosonic string propagator,
including the possibile presence of D-branes, by discretizing the light cone
worldsheet on an M times N rectangular lattice, with M proportional to P^+ and
N+1 proportional to ix^+. The integrals over the moduli then become sums which
we evaluate numerically. The main purpose of this study is to assess the
reliability of the worldsheet lattice as a regulator of the divergences in
string perturbation theory. There are two natural geometrical counterterms for
the lightcone worldsheet, one proportional to the area of the worldsheet and
the other proportional to the length of worldsheet boundaries, tracing the ends
of open strings. We show that the divergences in the closed string self-energy
can be cancelled by the area counterterm and a renormalization of the Regge
slope parameter. The residual finite part is compatible with Lorentz
invariance, provided a novel regularization, natural to the lightcone
worldsheet lattice and described in this article, is employed.
