Yes, a contract to lease is binding in Louisiana. Regardless of whether the lease is verbal or written, as long as the landlord and tenant agreed upon the terms, rent, and property, the lease is legally binding.
Even if there was an agreement to start a lease at a later date, it is still considered a binding agreement as long as both parties are aware, informed, and understand the terms (LA Civ Code 2670 (2018)).
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The information for this answer was found on our Louisiana Residential Lease Agreement answers.