LOVE IT!

I think I might've just got this in our campaign - yay!!

Is it reusable? IE, if it runs out of oil can you add more and still reveal invisible?

Yes, the wording implies so.

This is super powerful for it's level... I would make it use special oil or up the rarity of this

Use the Control Flames cantrip to double the bright light and dim light so.... 60 bright and additional 60 dim...

The illustrations, I'm pretty sure, is a bullseye lantern.

@Killuo_Divinely

"You choose nonmagical flame..."

This is a magic item, thus Control Flames wouldn't work on it.

Can this reveal things that are in the Ethereal plane, as See Invisible does?

"Invisible creatures and objects are visible as long as they are in the lantern's bright light"

Does this reveal "hidden" things like a rogue in Stealth "mode" or just only the invisible condition?

Quote from haldir77 >>

"Invisible creatures and objects are visible as long as they are in the lantern's bright light"

 

Does this reveal "hidden" things like a rogue in Stealth "mode" or just only the invisible condition?

 

 Just the invisible condition. If an invisible rogue is also hiding behind a bush, you're still not going to be able to automatically see them with this lantern. The lantern gives you the chance of perceiving them as if they weren't invisible, that's all.

Quote from ConfessorAmnell >>

@Killuo_Divinely

"You choose nonmagical flame..."

This is a magic item, thus Control Flames wouldn't work on it.

The item may be magical, but that doesn't necessarily mean that the flame is. The light could become magical as it leaves the lantern, or it could magically influence invisible entities directly. It's up to the DM at the end of the day.

Do this allow you to see the Scrying orb if lit? 

Yes. In the description of a scrying it says “On a failed save, the spell creates an Invisible sensor within 10 feet of the target.” 

it's pretty good

Could this be used to see shapeshifters like Truesight, let’s say against changelings or Whisper Bards?

No, just invisibility

Would this reveal scrying if the focus of the scry was within range of the lantern? 

Neat.

Is it alive?  Because of the eye it looks sentient.