it actually should be issued instantly. I change my flight last weekend, originally for 3 Sep to now end of May 22. It was re-issued immediately (i.e. within less than an hour). Your situation is not normal and has nothing to do with "high volume" or so, as the process is mostly fully automated.

If the ticket is not re-issued, you usually will not be able to book seats or upgrade, if you indend to do so.

I suggest calling again or contacting the LH Lurker. Feedback thread for the official LH Lurker(s), LufthansaGermanAirlines