They are not required for your AADSAS to be complete, and as such, the ADEA will submit your application to dental school (when complete) even if you don't have any LORs submitted. So technically there is no "due date".
How it works is, you start your application, and there will be a section called "Evaluators (LOE matching form)", where you'll designate up to 4 people who you expect to receive letters from. Futhermore you will also designate whether they'll be mailing in the letters or submitting electronically (your writers will be contacted by their email addresses, that you provide).
It's a good idea to do this step early (you'll likely want to have at least 3 letters submitted before your app is sent out, if you and your writers on on top of things, this should be easy). Follow up with your writers once you've completed this section in AADSAS to make sure they received the instructions for submitting their letters. Once they've submitted a letter, you'll be able to see that they submitted it in your application.
Edit: In case you're wondering: if your app gets sent out, and then you receive an LOR, it will be sent out as an update to your application to schools weekly.