This is how it works with Sixt indeed. You can not fill in a discount code, but you will have a discount connected to your customer profile.

So you need to apply for the Sixt card and send a scan of your airline card, then your discount will be automatically taken into account.

It does work: I have had a standard Sixt card for years, without really using it. Since I wanted to book a couple of cars for the weeks to come, I have sent a copy of my LH Sen card yesterday late night to Sixt, this morning early I got the message that my card had been upgraded to Diamond and the discount would automatically apply. And yes the rates are lower now.