@ Matt LorenzoI would definitely not accommodate the security deposit as the last months rent. 

The OP is in Chicago, but I'd be interested to hear people's take on the following.TX Local Government Code Sec. 250.007 (a)Except as provided by this section, a municipality or county may not adopt or enforce an ordinance or regulation that prohibits an owner, lessee, sublessee, assignee, managing agent, or other person having the right to lease, sublease, or rent a housing accommodation to a person because the person's lawful source of income to pay rent includes funding from a federal housing assistance program.

If they can get out and you can re rent without a loss of time or money, why wouldn't you accommodate them?

Text him back and inform him that the lease is invalid since he lied when filling in the application, regarding 3 additional people in the unit, and that he will need to find alternate accommodations.

Our service animal agreement is similar, but doesn't ask for additional rent or security deposit (replaced by validation requirements regarding the need for reasonable accommodation, proof of disability and the need for a specific animal).

The term market rent is intended to reflect what tenants are paying for comparable accommodations and tenants know that.

Some want it run the first day of the month and others want to wait until their first payday of the month and we accommodate that as well. 

At first, I tried to accommodate them, but after a month of complaining, I gave them the option to move out with 30 days notice so I could find a new tenant. 

Exactly what she offered and you're accommodating a hard to place dog.

Free accommodation for the rest of the tenants life?