Earlier is better, for many reasons. If at all possible, shoot to have your letters submitted for uploading by the first week of September.
As soon as you submit your application (hopefully right after labor day), some programs will review it. If you're lucky, you'll start getting invitations for interviews in early October, a full month before programs will receive your dean's letter. Some programs (e.g. Penn) will extend all of their invitations at that time.
A letter from a Sept/Oct rotation is too late. Even though you might beat the published deadlines, such a letter would put your application in the "incomplete" pile for a long, long time, which would effectively cause you to get lots of rejections.
My advice is to start looking for another LOR now. If you can have three letters submitted by mid-Sept, you'll be sitting pretty. Should you happen to get a stellar letter late in the game, you can add it as a fourth letter to your (already) complete application.
Good luck,
doepug (MS IV)