Most programs only accept letter submitted from ERAS (so i was told, anyway). Even if your new letter is written and sent out, it will take a couple of weeks for it to be scanned into the system (again, my personal experience -- one of my LOR's was received by the ERAS postoffice on 10/16 and was added to my file on 10/27). Most programs close application cycle on Nov 1st, so your letter may not even get to them, unless you convince the program coordinator to let you fax or email it in.
If you're trying to get that letter to programs like Lenox Hill, that has a deadline of Dec 8th, you can try to go through ERAS -- if one of your original letters was not downloaded by the program, you may be able to replace it with the new one. Check the ERAS FAQ section.