Yup, LH selling "full fare flex" F tix that aren't flexible at all is false advertising at the least, fraud at worst.
While I finally got my one-day change, it took two weeks and no small amount of time spent on the phone over this.
One would think that LH would want to keep its highest yield and most profitable customers happy with extremely small changes that are promised at the time of purchase, but all they've accomplished is that I'm now looking to book with AF for full fare first revenue tickets for upcoming flights. While the FC line is great for shortening the wait times for calls, if getting Y (or no) service is the result, why have a FC phone number at all?
Congrats, LH, your stupid intransigence is now costing you real cash because you couldn't accommodate a change for a full F customer that would have cost you, literally, NOTHING.