How Can I Correct the Short Lateral Incisors? Can They Move Down?

First of all you should discuss your ultimate desire. Is it to have the laterals the exact same length as the centrals, even though that is not considered "ideal"? If so, placing buttons and using rubber bands might bring down your laterals some more.

If the orthodontic movement is already complete and you have anterior contacts with the lateral incisors.  You may want to consider some chairside bonding or porcelain veneers to achieve the look you desire.  Good Luck!

It appears that your lateral incisors are disproportionately small. If you tilt the clincheck up so you can see how the lower incisors are contacting the upper lateral incisor... if they are in contact, you cannot move the lateral incisor down. If this is the case, you may want to line up the gum line, get the right proportions for the anterior teeth and maybe consider veneers to get a harmonious balance.