Hi Clint,
We issue
Certificates for a completed course. This is a 3rd party add in. It has some conditions which can be turned on, involving quiz and survey. Emails upon completion to student and teacher are a feature.
As of yet there is not a
Groups setting for a Lesson in a course. Might involve a lot of work moving students from group to group. For example a report that showed only students who were part of the enrolled group in a course.
We also use a version of
Activity Locking (both a generic term for 3rd party Conditional Activity modules, and a standard module in development for 2.0 ). Some 3rd party versions will both hide
activities (such as a lesson) from a student if conditions are not met, and mark activities which have been completed. This does not help the teacher

Following up on Sandra's method, remember there are
Reports which can tell the teacher which students have completed the assignment or received a certificate in a course. Sandra mentioned
Grades or the Gradebook which is essentially a report.
Your other topic, got me wondering if "My Moodle" or a student's course block might show an icon like a diploma or certificate when a course was done. Good questions.
Hope this helps Chris