PN,
Lanchester's laws of combat are only partially applicable here. E.g., the N (north) side will definitely fire not against the S-side "guns" but rather at "squares" (including cities, industrial areas and military bases) because their accuracy is very poor.
But in the part where Lanchester works, it says that the number matters.
So, as KenV correctly wrote, the question is how many rounds the N-side could make? If they have thousands of "guns" and some are manoeuvrable (and some can quickly hide underground), I am not sure that all of them would be supressed in two rounds...