N reg might be an answer for some as the FAA have their own type certificate.
Good suggestion, however................... is not the FAA Type Cert dependent upon EC (in this instance) accepting responsibility for the airworthy standard?
The Americans have their own way of doing things so..........
I'm not fully sure, but you might be able to register individual Lamas as national "experimental aircraft" in order to keep some of them flying after 1 Jan 2020. They would (of course) be private-only, but the surviving aircraft would be of great sentimental value.. just imagine hearing that old Artouste engine slowly spooling up when the other ships are long gone!