They want it so that if your landlord is or becomes behind in the payment of assessments they can seize the rent to pay the assessments. The lease is not public record and they have no other way to get it. They probably tried to get it from the landlord and were refused.
Unless the Declaration of Condominium give the association the authority to approve tenants, I would not give them a copy. Ask them to prove they have the authority to see it.
This communication is not intended to create an attorney/client relationship. It is always recommended you consult an attorney in person to discuss your case. The Law Offices of Stage & Associates practices state-wide and represents homeowners and community associations. Please visit our website at www.stagelaw.com.