Carvedog cited the applicable regulation.
Operationally, after winning the lottery, the permit holder makes out an application for the launch permit (a physical piece of paper that you'll have to show the Lees Ferry ranger). Your launch date is already established by the lottery, of course. You have to specify your takeout date and location (Diamond, Pearce, or South Cove) on the application. There are no lines, blocks, or spaces on that application for more than one run, and it must be a downstream trip.
When you receive your actual permit, it will authorize you to take the trip as outlined in your application. Any variance from that approved itinerary, you're at risk of some kind of law enforcement action. End of story.