My 218 S-Tronic has just moved to the "preparation" stage today so it doesn't look like a fault. Not heard of any supply issues either on any of the forums here or in Germany. Given that, it may just be this is your lease provider using it as an excuse for being unable to source the car for some other reason.
There does appear to be an issue with the S tronic gearbox. Not sure if it applies to other models but I've also ordered the 218 quattro S tronic.
Fed up of no movement on order so called Audi UK customer services directly. They advised there was a problem with the S tronic and this was delaying certain configurations. Apparently the issue is now resolved but they're playing catch up.
Ordered 25th October with initial est build week 4. Used the Audi online tracker and established build week 18. This has now changed and site says car will begin construction this coming Monday 11th.
That's interesting, I ordered mine at the beginning of March (although the dealer had actually put the order through for it early February) and I got a build week of 16 (i.e. week beginning 18th April). I've had no notification of any delays and its just moved to the preparation phase today and still showing build week 16 so doesn't appear to have been affected by any delay if there is one.
Seems a little strange if it is just "certain configurations" as other than the engine variant I can't think of any thing else that would impact the S-Tronic. We're all talking about the 218 here although in my case its a quattro, I wonder if that's the difference?.
Given that my order is relatively recent you'd think I'd be at the back of the queue if they are playing catch-up on this but I don't seem to be, strange....