Hello,
I am the Aftersales Manager at Lexus Leeds, I would like to take the opportunity to clear this up for you.
The licence key is certainly a physical part (a plastic scratch card) and is ordered from Lexus like any other part, unfortunately, they were on a major back order for a long time - circa 3 months. They are now available to order and I hope this has now been completed for you.
All the best & enjoy your NX.
Jordan