LÖVE

I would like to press a key and have my love2D program respond without me first focusing the love2D window by clicking it. Would be useful for, say, a livestream visual that I can alter with a key press.

Doesnt look like it.
If youre the only user a quick hack in would be to just read from /dev/input in a thread.
I am not aware of other simple ways, let alone one that universally works.

While keyboard and mouse won't really work like that, you can try whether gamepad input works when unfocused, that has a higher chance i think.

There's always the option to poll the keyboard through FFI, but that's OS-specific. For example, on Windows you can import and call GetAsyncKeyState to query the state of a key.