If your ball is lost or out of bounds you may drop a ball in the vicinity of where your ball was lost or out of bounds (including the nearest fairway area), under a two-stroke penalty.
You may still opt to play a provisional ball before leaving the spot where you played your last shot, whereby the provisional ball would become the ball in play should the original ball be lost or out of bounds. The Local Rule would not be available in this case. But since the Local Rule permits you to drop your ball within two club lengths of the fairway edge it would have to have been a really poor shot (think shank or no distance) for the golfer not to take advantage of the Local Rule.
For the avoidance of doubt, if you hit your ball out of bounds from your tee shot and you take advantage of this Local Rule, when you drop your ball in the relief area “C” in the above diagrams, your dropped ball is now in play and your next stroke will be your fourth, as if you had played “three off the tee”.