Let it be known that the vast majority of third-party controllers will not support all of Luna’s features. As noted by Android Central, you can technically pair any Bluetooth controller to Luna, but the buttons may not not map correctly (i.e. “X” corresponding to “A”), turning your chosen controller into jumbled mess.
While those options are the only confirmed non-Amazon fill-ins for the Luna controller, that doesn’t mean others don’t work.
Controllers like the SteelSeries Stratus XL and the SaharaMirco are both compatible with Amazon Fire TV, so there’s a chance they’ll translate to Luna, but it’d be shame to waste money without knowing for sure.
Unlike the Xbox One and DualShock 4 controllers, Amazon’s Luna controller connects via Wi-Fi instead of Bluetooth. In theory this reduces latency, but it also means that the way you connect is slightly different.
To connect your game controller to Fire TV, open the Fire TV menu, select “Settings,” then, “Controllers and Bluetooth Devices,” and, “Game Controllers.” Now select, “Add a new game controller.” Put your controller into pairing mode and wait for your Fire TV stick to find the device.