I signed a six month lease and needed to terminate it one month early (may 1st instead of June 1st). I only gave my landlord about two weeks notice and she claimed that I must pay the fees for her to use a property management company to place a new renter because of the short notice I gave her. I paid this fee. She also claimed that I needed to pay her for the month of May because she could not find a new tenant till June 1st. However, when I contacted the property management company, they said the new tenant signed their lease May 1st and started moving their things in. When I confronted her, she said that they started moving things in but did not start paying rent till June 1st. Do I have an obligation to pay her for the month of May if there was already a new tenant under a new lease?

Yes. They may have signed a new lease effect June 1. But since you broke the lease and vacated earlier, the landlord was within their rights to allow them to start moving their things in.

On the other hand, you might be able to fight her on paying the fee for the management co. Since she would have had to pay this fee regardless in a month's time.