Lufthansa can be touchy when it comes to visiting their premises in Frankfurt. I once was invited to a tour through Lufthansa Technik's maintenance hagar, but they wouldn't let us see the operations centre, although we were accompanied by a senior captain and fleet manager. Maybe the best course would be to send them an e-mail, explain your background, and just ask if they were offering any tours.
Within the Frankfurt CTR there is a smaller aerodrome, Egelsbach (EDFE), which is worth a visit. They have an excellent restaurant. Another idea would be a a bus tour over Frankfurt's apron. You can buy tickets in the terminal.