Does a med spa have to register or hold a license in Louisiana?

Short answer
Not directly — the cited rules create no "med spa" license as such; they do require a license for any facility where cosmetology or esthetic services are offered, and an individual medical license for anyone practicing medicine there.

Louisiana licenses the PREMISES, and the legislature said so in the purpose clause: the licensure of all persons who perform cosmetology, of all facilities where cosmetology is taught, of all facilities where cosmetology services are offered, and of all persons who supervise individuals performing cosmetology, are declared necessary to ensure that only qualified persons practice at facilities meeting appropriate standards. A “beauty shop” or “salon” is any premises upon or within which cosmetology is practiced for a fee — expressly excluding premises where the persons exempted by R.S. 37:581 practice or do business, a section these claims do NOT survey. Cosmetology itself is defined by means and by component practice: using the hands, mechanical or electrical apparatuses or appliances, or cosmetic preparations, in any combination of esthetics, hair dressing and manicuring for compensation. Esthetics is an enumerated list, and it reaches micro-dermabrasion, epidermabrasion and particle exfoliation. The fee schedule is in the statute itself: each initial certificate of registration and each annual renewal costs $35.00 for a cosmetologist, esthetician, manicurist, teacher/instructor or manager and $55.00 for a beauty shop or salon, mobile salon or home care, with $50.00 for the initial inspection of a salon, mobile salon or booth rental and $50.00 for a booth rental, special or temporary permit; an expired certificate restored within three years costs twice the applicable fee for each year expired, not to exceed three hundred dollars. On compounded drugs the Board of Pharmacy’s rules answer the GLP-1 question by DEFINITION: compounding does not include the compounding of drug products that are essentially copies of a commercially available product — a copy being the same active ingredient in the same, similar or easily substitutable strength by the same route, with a change of less than 10 percent not counting — and a pharmacy may prepare a variation only where a prescriber documents a clinically significant difference on the prescription and the pharmacy does not prepare copies regularly or in inordinate amounts, or a copy where the product is discontinued, on the FDA drug shortage list or temporarily unavailable. The rules apply regardless of the location of the patient, a practitioner’s office included, and define practitioner administered compounds as products compounded on a prescriber’s medical order for administration by the prescriber.