PSA: The Onion Doublet set is still obtainable as of patch 6.38.

I know there's been some posts on this topic before, and speculation that the set was removed in patch 5.4. At least for the Onion Doublet set, this is not the case (cannot speak for the Red Onion Helm or Peregrine Helm.)

https://i.imgur.com/2Jkbn18.png

I just recently reset my retainers' levels in order to try for this set as well as the Red Onion/Peregrine helms. By keeping their levels below 50, you keep them in the ARR loot table, thus greatly increasing your odds since you don't have to worry about rolling random dungeon gear from the expansions. I have been playing since late Stormblood and this is the first time I've seen a single piece, with 5 retainers, almost exclusively being sent on quick explorations. However, this is the first time I've reset them like this with this in mind. So perhaps they are just incredibly rare regardless, or only abysmally rare if they're at max level. I can't really say for sure. Keeping them below 50 will definitely increase your odds, I just don't know the exact figure.