How does a neutral wire add any protection from near-by lightning strike
The induced pulse from a nearby lightning strike is a common-mode signal with respect to the power line, which is a balanced (differential) connection to the pole transformer. (I'm assuming that you're in the USA, with the usual 120-0-120 "split phase" power connection.)

The neutral is grounded at both ends &mdash; i.e., at the pole transformer and at your service entrance. At least one connection is required to keep this link from "floating" to arbitrary voltage levels with respect to ground. Two connections serves to short out the common-mode surge from lightning strikes. 

In other words, if the neutral (center tap) was grounded only at the pole transformer, the common-mode surge induced along the length of the cable would enter the house, rather than being shorted to ground. Similarly, if the only ground was at the service entrance, then the pole transformer would experience the surge, possibly exceeding its ratings and causing an internal breakdown.