I doubt that will be supported. You're right, J1772 doesn't support 277VAC, NACS does. However, even there, I think (some) Tesla brand EVSEs are the only ones that have ever supported that, and Tesla has shied away from advertising that recently. Similarly, to my knowledge, only Tesla cars have ever supported 277VAC. It doesn't just require the different connector, it requires different hardware in the car's onboard charger. I'm not clairvoyant, but Lucid's switch to NACS was pretty last minute in terms of the Gravity design, I would be surprised if they changed the internals that much for something hardly anyone would ever use. I think you'll need a transformer.
On another note, if this is a shared apartment building garage, are you even allowed to install a charger? Or are you asking about mobile chargers?