Can I set a default "lights" per device in the Home app so that controlling the lights is more like on Star Trek (TNG)?

1. In the Shortcuts app, create a shortcut.
2. Add a single action to it to ‘Control <House Name>’ and turn on your desired light(s).
3. Title the shortcut exactly "Turn on the lights".

Now ‘Hey Siri, turn on the lights’ will run your shortcut, bypassing the default Home behaviour.

Shortcuts sync across iCloud devices so your new command will be available everywhere (you might have to open the Shortcuts app once for it to be aware). If you want to use the same shortcut everywhere but do something different, you can use the Get Device Details action and switch on something identifiable per device, e.g. Device Name: