My rear license plates have factory screws and cannot fall off. In fact I haven't seen any cars that is not setup from the factory. Only in the rear. I guess it's possible that Lamborghini Newport Beach installed the mounting plates, however I saw them when the car first came in and was being unwrapped.
Greetings and salutations and welcome to Lamborghini Talk, Bully69!
I'm interested in knowing how a plate fell off. Was it not screwed on? As Russk pointed out, that is the usual procedure. I've never heard of this happening on the rear plate...the front plate, maybe, if the car doesn't have a proper mounting frame to accommodate a plate (as some cars don't since their state/province doesn't require a front plate), but I've not heard of such an issue with the back plate.
Are lost plates a common issue in Australia? I would imagine that the 3M tape is how most if not all plates are mounted? I think this is normal practice in the UK as well. Here in the states, all of our plates are mounted with screws, so we don't have this issue.
I would try the 3M exterior mounting tape. I had the side door molding come off on a car I had, and this stuff worked very well. Held through all kinds of weather with no problem.