I don't know when I should apply?

I’m a junior right now, but I only need 3 more credits to graduate, so I’m going to take those during the summer and graduate in August 2016. I really want to start college next year, but I don’t know when I need to start applying for financial aid and the school I want to go to (Lee university). Do I apply for fafsa and Lee during the summer of next year or sooner?

If you do intend to become a future doc I would recommend not graduating early but taking some dual enrollment or AP classes next year. That will give you a better background to do well in college. If you are determined to graduate in August you need to call Lee and talk to them. They may not accept you until a year later which would mean you would take a gap year and do something else (like work or travel or volunteer).

Contact Lee University, explain your situation, and ask what to do. My guess is that you should apply now.