This is similar to Texas where it just says something like the plate needs to be "near the rear" of the vehicle. I searched cases, etc. and could not find anything saying that Louisiana license plates must be horizontal. Though your law does not require it to be horizontal I guess a judge or cop could say it is not "clearly legible" if you have it on there vertically.
This is the Louisiana statute below:
§ 507. Display of plate
A. The permanent registration license plate assigned to a trailer, semitrailer, motorcycle, or other motor vehicle shall be attached to the rear thereof. Notwithstanding the foregoing, the permanent registration license plate assigned to any truck having a gross vehicle weight in excess of six thousand pounds or to any dump truck may be attached to either the front or rear thereof. For the purposes of this Section, dump truck means any truck with a bed that raises to dump a load. The permanent registration license plate shall be so displayed during the current registration year, except as otherwise provided herein.
B. Every permanent registration license plate shall at all times be securely fastened to the vehicle to which it is assigned, so as to prevent the plate from swinging, and at a height not less than twelve inches from the ground, measuring from the bottom of such plate, in a place and position to be clearly visible, and shall be maintained free from foreign materials and in a condition to be clearly legible.