I season my cast iron by cooking bacon in it so that probably won't work for your grill. But you could use a canola oil spray on both sides and then place it over a hot flame. That should help retard rusting.

is this a lodge double sided pan/griddle and (dumb question) is it the pre-seasoned variety they sell?

If not, then yes you should season. the same way you would a pan.

I'd say yes - at the very least, it can't hurt :-) I always season cast iron cooking equipment. It will likely make it a lot easier to cook and griddle on it.