Do I need to give my landlord a 30-day notice if my lease does not state that I do?

Usually, you must follow the terms of the lease. I do not know the terms of your lease, but does it give any indication of the requirement of notice before moving out? If it does not give any amount of time required to give notice of move out, then technically I would say that you are right. If she wanted a 30-day notice, it should be clearly stated in the written contract (lease).

The problem is your landlord may keep your security deposit or sue you in court for the remaining rent that she thinks is due. I do not know if she could win in court, but the judge may assume that you should have, out of common courtesy, given a timely notice to the landlord. It depends on how much notice you have given her and if she can quickly rent your apartment since she cannot collect rent from you if she collects rent from a new tenant. It's a situation that can go either way depending on all the facts of the case.