you can just ask them to prepare a LOR in advance and when the official app opens have them just send it in, that way you're not waiting months after it opens for them to submit it. personally, in my case, i asked 3 people for LOR's beginning of June, the first one was received late july, i missed the UCSF deadline cos none of the other two had sent theirs in, one was received a week after that, and the last one was received in late october...
so my advise is to ask early, and keep reminding and inquiring until it gets done because more likely than not the people who you ask for LORs will already have a busy schedule and things get pushed aside if they're not reminded constantly