There is currently not a feature that allows instructors to set a due date for viewers to complete a lesson. However, there are several ways around this.
Option 1: If you have communicated the due date to the students, but are concerned that students will try to take the lesson for credit past the due date, you can verify the date and time each student took the lesson in the Analytics. By downloading the CSV analytics file, you are able to filter and see if any students completed the lesson after the due date. More information on Lesson Analytics can be found here.
Option 2: Setting a due date can be managed by using an LMS, like Canvas or Blackboard. Lessons can be linked to inside of an assignment or module with a set due date by embedding the lesson or adding it via LTI. The embed code does not require viewers to create a Zaption account, but the Zaption Pro LTI integration requires a viewer login. If you don't have an LMS, sign-up for a free account with Schoology. It's a great tool for individual instructors, and you can set a due date within the LMS and link to lessons in assignments.
We definitely recognize the need for this feature, and are constantly working to make sharing lessons more seamless and intuitive.