This is 3 Nephi 9:9-11 and it gives the most information on what the Lord's criteria was:
9 And behold, that great city Jacobugath, which was inhabited by the people of king Jacob, have I caused to be burned with fire because of their sins and their wickedness, which was above all the wickedness of the whole earth, because of their secret murders and combinations; for it was they that did destroy the peace of my people and the government of the land; therefore I did cause them to be burned, to destroy them from before my face, that the blood of the prophets and the saints should not come up unto me any more against them.
10 And behold, the city of Laman, and the city of Josh, and the city of Gad, and the city of Kishkumen, have I caused to be burned with fire, and the inhabitants thereof, because of their wickedness in casting out the prophets, and stoning those whom I did send to declare unto them concerning their wickedness and their abominations.
11 And because they did cast them all out, that there were none righteous among them, I did send down fire and destroy them, that their wickedness and abominations might be hid from before my face, that the blood of the prophets and the saints whom I sent among them might not cry unto me cfrom the ground against them.
So it looks like he didn't have a very high standard. The ones that were destroyed:
1. committed secret murders and participated in secret combinations.
2. because they destroyed the peace of the people and the government of the land
3. they had cast out and stoned the prophets the Lord had sent to warn them.
4. apparently they had killed prophets and people who believed in God.
5. They had cast out all the righteous among them.
I can only conclude that people that didn't participate in these things were saved.
In 3 Nephi 9:13 there is a little information about the ones that were spared.
13 O all ye that are spared because ye were more righteous than they, will ye not now return unto me, and repent of your sins, and be converted, that I may heal you?
