When you assign a lesson you can set when it opens and when it closes. Both are optional: leave them blank and the lesson is open from the moment you assign it.
Setting the dates
Open the lesson from My Library and click Assign.
Tick the classrooms you want. Each one gets its own Start Date and End Date, so the same lesson can run on different dates for different classes.
What the dates do
Start Date. Before this, students cannot open the lesson.
End Date. After this, the lesson closes and no more work can be submitted.
The field is called End Date, not "due date". Both can be changed later: to give a class longer, open the same dialog and push the End Date out.
After the end date
Work already submitted is unaffected and still yours to mark and return. To let a particular student back in, use Enable resubmission on the assignment. See Enable resubmission for a lesson.