Tesla sells a J1772 EVSE. So, you could use the Tesla adapter that comes with the car and the J1772 for the Lightning. I see that it's $125 more than the Tesla Wall Connector. I don't think it was that way a few months ago.

J1772 Wall Connector
Our J1772 Wall Connector is a convenient charging solution for Tesla and non-Tesla electric vehicles alike, and is ideal for houses, apartments, hospitality properties and workplaces. With up to 44 miles of range added per hour, a 24-foot cable, multiple power settings and a versatile...