The Great Vault did not recognize Heroic Castle Nathria kills. Last week, I killed all 9 LFR Bosses, and 2 Heroic Bosses in Castle Nathria. I only had a choice of 2 ilvl 187 pieces of gear, when I checked the vault today (I did loot last week, so that is not the issue here). That is 11 boss kills and only seeing 2 LFR pieces to choose from for this week.
Were the heroic bosses different bosses than the lfr bosses?
No, Heroic were Shriekwing and Huntsman. So there would be overlap.
That would still count as 9 bosses then. The heroic bosses would just replace the same lfr bosses you killed, and I believe you would need to have killed one more heroic boss to increase the Item lvl of one of the items in the great vault.
So, help me a bit here. Based on that, which I understand, we need to kill a minimum of 3 bosses on a given difficulty for the Vault to change the Item lvl. I was under the impression that it was an average of the content run.
Is that your understanding as well?
My understanding was that it was 3 raid bosses of the same difficulty, to get that Ilvl in the great vault, tho I’ll see if I can find the article concerning this.
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Ok, I will go find an article for further clarification, but I do want to thank you for taking the time to respond. That helped immensely. 
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Was this the page, Praetorian?
https://us.battle.net/support/en/article/281236
It covers a bit of how it works.
Wowhead also have a guide.
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Yes that was the page 
I just came back to post it thanks Vrakthris 
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I completed all the bosses in the 3 wings of lfr (9 bosses) and the reward listed was for 3 bosses. I looked at notes on support and a post recommended doing a ui reset so I logged out and back in again, and now there is no reward at all. This seems to be broken…