  We calculate the long-distance radiative corrections \delta^e_{LD} and
\delta^{\mu}_{LD} to the K^0 -> \pi^- e^+ \nu_e and the K^0 -> pi^- \mu^+
\nu_{\mu} decay rates. This analysis includes contributions to the
long-distance radiative corrections from outside the kinematically-allowed
three-body Dalitz region and tests the sensitivity of the radiative corrections
to the hadronic K-pi form factors. A program, KLOR, was written to numerically
evaluate the radiative corrections and to generate Monte Carlo events for
experimental acceptance studies. The K^0_{e3} and the K^0_{\mu 3} long-distance
radiative correction parameters are determined to be (1.3 +/- 0.3)% and (1.9
+/- 0.3)%, respectively. We also present predictions for the fraction of
radiative K^0_{l3} events satisfying various requirements on final-state photon
kinematics.
