You can always lerp the positions. Use an variable to store the target x position for the box (lets say "goToX") and when you press the left/right arrow keys subtract/add to this variable the 130 pix offset (you'll need to find a way to limit me minimum/maximum x position). Then, add an event that does the following:
every tick-----> Box | set X position to lerp(self.X, goToX, t)
where t is a number between 0 and 1. The closest to 1, the "snappiest" it will get.