Assessing the lightning performance of real, extensive and highly branched distribution networks is computationally demanding: it requires coupling the electromagnetic field to the line for a large number of Monte Carlo events. This paper proposes a three-stage acceleration method that reduces that burden without compromising accuracy. Events are first pre-screened with an analytical estimate, so only the hazardous ones reach a full coupling simulation. The illumination is then bounded to a distance threshold, with the remaining line represented by a frequency-dependent model that preserves the reflections of the branched topology. Finally, for networks that do not fit in a single case, an optional stage partitions the network into sub-networks solved independently and reconstructed. Every threshold is calibrated against a full-fidelity reference on the same strokes, and the values found are offered as a conservative suggestion for this feeder. Two further elements are addressed: an exposure buffer following the network geometry, and a stopping criterion. The method is evaluated on a real 13.2 kV rural feeder of 116 km spanning about 24 km × 24 km, with an exposure area of 178 km². The acceleration acts on the indirect strokes, the only ones that need the field-to-line coupling; the direct strokes are simulated and reported separately. The computational cost falls by more than one order of magnitude while the error of the exceedance rate of the indirect strokes stays about 1%, and an independent 200,000-stroke campaign confirms statistical consistency. Convergence should be judged from the number of events above the voltage of interest, not from the apparent stabilization of the estimate.