Legal Question in Landlord & Tenant Law in Louisiana

It depends what the lease says. Normally, in a residential lease, the landlord is responsible for all repairs, including HVAC, if it goes out at any time during the lease. The only usual exception is when the HVAC repairman shows that the damage was done by the tenant, for example, because they never changed the filter. If the tenant caused the damage, the landlord can usually charge the tenant for damaging the AC. Again, the first place to look is your lease, as it is the "law between the parties" and will control.