Landlord and tenant law in Illinois is found primarily in the written lease as well has in statutes and ordinances at the local, state, and federal level. In Chicago, the most far-reaching of these is the Chicago Residential Landlord-Tenant Ordinance (RLTO).
You are correct that a lease, much like any other contract, does not require performance by one party until that performance's duty arises. In a lease, the landlord provides the apartment, house, etc. in exchange for the tenant's duty to pay rent. That duty arises when the lease says it arises -- in your case, apparently on the 15th of each month. Therefore, the landlord does not have a legal right (under the facts as you provided them) to payment before.
Now, the RLTO comes into play if the landlord attempts retaliation for not paying the rent on her new, unwritten terms. Occasionally an unscrupulous landlord will make life difficult on a tenant that does not play by her rules on a variety of ways, such as lockouts, unlawful attempts at eviction, taking or detaining the personal property of the tenant, and sometimes "adjusting" utilities to the tenant's unit. If anything like this should occur, a good landlord-tenant attorney should be consulted to assist in remedying the situations through court action.
In the meantime, I would suggest just reminding the landlord politely that rent is not due until the 15th of the month. It sounds like your landlord does not have any ill will, but rather is just trying to make ends meet. Ask her what "need" means, and if you feel that she is infringing on your rights as a tenant seek the advice and counsel of an attorney or one of the local Chicago tenant's associations.
NOTE: This answer is not intended to be legal advice and should not be construed in that way. This answer does not create an attorney-client relationship and no such relationship may be created absent a signed retainer agreement. The author is licensed in Illinois only, and his answer is for educations purposes alone.