The terms Jr., Sr., III and the like used after a person’s name are part of the name and thus generally do not take a comma:

Lonnie Poole Jr. gave a generous gift to the university.

If a person requests that we use the comma with his or her name, we should grant the request out of respect for the individual. Absent such a request from the person whose name is in question, we should follow our style and omit the comma.