Curate, connect, and discover
I think the last option makes the most sense, but personally I think it’s that the planet that was destroyed was the lantern’s jurisdiction and he died before being able to tell the rest of Oa. They might be on their way, but most likely it would take some time, given that the conquering the the planets is very recent, still nothing yet, but soon.
That might also be true for the hawk people, with them most likely escaping since we saw they had times to make carving of the event and are also probably on their way.
Also I think that computer was the most life given the fact that he could cry.
I don't know a ton about the Green Lanterns. I know some but not nearly as much as other areas of the DCU. I hope that someone who does know them well enough can help me figure this out.
So the GL corps sent a Lantern to stop Brainiac's invasion and Brainiac made Kara kill it and turn the last remnants of it's consciousness into a hologram copy.
But the ring still works for the hologram copy? How does that work? I thought they were powered up by the wearer's strong will. How can he have enough of a will to make the ring work if he's just an echo of what he once was? Is there a precedence for something like that in the comics?
The Lantern corps would have sent more Lanterns if one of them were killed on their mission right? But if Kara had wiped them all out wouldn't Oa be on her list on conquered planets?
Or do you think there ARE more Green lanterns on the way? That they're currently just strategizing a way to beat Kara and Brainiac's Empire.
Or do you think Brainiac is allowing the holographic copy to have just enough will to use the ring and send messages back to Oa to tell them, the situation is being handled, don't send anyone else, until Brainiac is ready to lure more out.
Finally, the family dynamic we need
Cousins annoying each other