NC law requires L to repair any AC unit supplied or required to be supplied. Therefore, even if the AC is not listed as an appliance, if it worked when you moved in L has to fix it. Send L a letter demanding he fix the AC. If he doesn't, ask the local court if you can pay your rent into the court until the AC is fixed. Many states allow this option as a way to force L to meet statutory repair duties. In my quick search, I did not find any repair & deduct remedies you could use. Ask L if he'd like you to pay someone to fix the AC & deduct the amount from your rent. (Use a licensed contractor, get a receipt, get the agreement in writing, & put a cap on the amount you can pay - usually 1 month's rent.)
§ 42-42. Landlord to provide fit premises.
(a) The landlord shall:
(1) Comply with the current applicable building and housing codes...
(2) Make all repairs and do whatever is necessary to put and keep the premises in a fit and habitable condition.
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(4) Maintain in good and safe working order and promptly repair all electrical, plumbing, sanitary, heating, ventilating, air conditioning, and other facilities and appliances supplied or required to be supplied by the landlord provided that notification of needed repairs is made to the landlord in writing by the tenant, except in emergency situations.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.