Minimum notice for not renewing lease?

Poor baby

unless you are in a rent stabalized apartment then there are no requirements. Did you actually ask prior to now if he was going to give you a lease? sounds like it is on you more then him. plus 40 days is about right as you can;t really look until a month before anyway.

Your lease has an expiration date on it. There is no need for your landlord to give you any notice. The law assumes you will move out at the end of the contract.

Unless your landlord absolutely must have possession on Day #41 (for example, because another tenant is moving in that day), ask if you can pay to extend your lease for a week or three. Trying to evict you and/or suing you for damages because you overstayed is a pain in the neck, even if the landlord will eventually win. If the landlord is reasonable and has the option, you may be able to negotiate a deal for a little extra time so that both of you can avoid a major headache. But do this quickly so you know what your options are.

Also look at your lease to see if there's a required notice period written into it.