I decided to recall when the other Raiding with Leashes achievements were added:
According to this, it seemed that 6.3 would be the next one, but probably there will be no 6.3,Raiding with Leashes (Classic): patch 5.1
Raiding with Leashes II: Attunement Edition (TBC I): patch 5.3
Raiding with Leashes III: Drinkin' From the Sunwell (TBC II): patch 6.1
so who knows, maybe 6.2.3 is that one?
Talking about Legion, I need to think a bit longer about that. ;P
We can guess so far that it will include first WotLK raids up to Ulduar.
(Deleted a list, as it was confusing the readers.)
I'd deny Vault of Archavon, as it's PvP-conditional. Naxxramas was a remake, included in its former tier and The Eye of Eternity is too compact.
Saying this, the main focus is Ulduar and maybe The Obsidian Sanctum.
I've even given already a name to the achievement: A World Worth Taming!
Well, but what could be included here?
I was told that some Ulduar-themed companions were already created as the part of promotion.
And a next lashling isn't something what could be my priority, even if there are only two B/B right now ingame.