If all letters are not in by 7/15 does that mean App will not be consider complete? Some programs like northwestern and u of c have 7/15 deadlines that is insane!
If thats the requirement of Institution then try your best to get the LORs uploaded ASAP. I believe, you should be able to send LORs later as well. You can also e-mail the program coordinator and ask about specific requirements.
good luck.