Is it correct for the official to deny A-3's request to occupy the third marked lane space during a free throw?

A player may request to occupy a marked lane space during a free throw, and under the rules of basketball, it is generally permissible for them to do so unless there are specific reasons otherwise defined by the rules. The official is expected to allow the player to occupy the space if they request it properly, without any infractions or violations present.

By denying the request, the official would be acting contrary to the established rules regarding player positioning during free throws. The rules facilitate a balance between offense and defense on the lane, allowing for a fair opportunity for all players involved. Therefore, it is correct to state that the official should not deny A-3's request to occupy the third marked lane space during a free throw, making the selected answer appropriate in this context.

The other options suggest conditions or requirements that would limit a player’s right to occupy the space, which are not supported by the standard rules governing free throws in basketball.