Make a checklist of the condition of the property and any furnishings when you move in. (Most properties will provide you with an inventory and condition form).A Texas lease agreement is a legal document that outlines the rental arrangement between a landlord and tenant. A Texas lease agreement is a contract that grants a tenant the right to occupy a residential or commercial property in exchange for the payment of rent. No information is available for this page. How to fill out the Texas Apartment Lease Agreement Instructions? Applicant's name (as listed on proof of identification). Applicant's former last name (if applicable). E-mail. Next, specify the rental amount and payment due date. This section requires a landlord to provide a tenant with a copy of the complete lease within 3 business days of signing.