If you mean for example, that your current term expires on August 31, and your landlord had you sign a lease today that begins on September 1, there is absolutely nothing wrong with that. However, I am assuming you mean that the terms overlap. If that is correct, it is a bit confusing, but I do not see anything not "legal" about it. Provided they are not expecting you to pay on both, I would say the new lease terminates the old lease. I am not sure what your goal is in asking this question, but you will have a problem arguing there is something illegal about this, since you voluntarily signed the new lease.
By the very nature of Avvo, you have only provided limited facts and no documentation, therefore, our response to your question is treated only as a hypothetical, and as such it is merely general in nature. You should not rely on this response in taking or forgoing action in your circumstances without discussing this matter with an attorney. If we had the opportunity to ask you sufficient questions and review relevant documents so that we were satisfied we had all of the relevant facts and circumstances, our response might differ significantly. Without the opportunity to ask you questions, and review all relevant documents and memoranda, we are simply unable to provide any form of legal advice. Our response to your question does not create any attorney-client relationship between us, and we are not acting as your attorney. We reserve the right to decline representation in any case. By answering your question, we are under no obligation to answer further questions. There are very specific deadlines for filing a lawsuit, replying to a lawsuit filed against you, or taking other action in order to preserve your legal rights. You should contact an attorney immediately in order to be fully advised of your rights, and so that you are aware of those deadlines. If you fail to act within the required time frame, you might be forever barred from asserting your rights or defending your position. The attorney answering this question is licensed in Illinois and Iowa only.