In LabTutor 4, is it possible to get a list of students who have or have not submitted an experiment?

Yes. The Status sub tab within the Student Data tab in the LabTutor Server admin pages allows instructors and administrators to see the status of all student experiments within a course. Search results can be narrowed down by searching within experiments, date ranges or by experiment status.

This information is valid for LabTutor v4.0 or later.