The short answer is: as soon as you are eligible. This way, if OSU's programs change some of their requirements you will not have to re-take classes or take different classes from the current program requirements. As a DPP student, you are an OSU student and will earn catalog rights once you have taken your first credit at OSU.
At the very latest, however, sign-up about a month prior to the start of the term
you'd like to begin taking classes at OSU.
Official DPP application deadlines page
When applying, request official transcripts to be sent to OSU for all of your college course work (all official transcripts need to come directly from the school that awarded the credits regardless if LBCC has received/evaluated them). LBCC will not automatically send transcripts to OSU for the application process; they need to be requested. If you completed the foreign language requirement by taking two years of foreign language in high school, you will need to have your official high school transcripts sent to OSU as well.