C. Terms of the Lease. A lease addendum is a separate legal document that allows a landlord to add additional information or make changes to a lease agreement.In an addendum to a lease, you will need to add the dates, names and addresses of all parties involved in the original lease agreement. A lease addendum is as important as the rest of the lease. When compiling the legal paperwork to add a tenant to a lease, you can create an addendum to the existing lease or create a new lease agreement. How do I fill this out? Gather the original lease and enter the details into the lease amendment, including, the name(s) of the tenant(s) being added or removed from the agreement. A lease extension addendum is a legal document extending a lease between a landlord and a tenant. A lease extension addendum is a legal document extending a lease between a landlord and a tenant. Tenant in Transitional Housing) to accept Supportive Services that are offered.