Comments posted to our Dark Souls 3 Wiki
So long as Siegward is in the kitchen, Greirat will survive the Irithyl Mission. If you go through the dungeon/kill Alva, but have not killed Yhorm and have any boss available to kill aside from Yhorm, you can still save Greirat if you have not yet rescued Siegward from the well. Rescue Siegward, send out Greirat, defeat a boss (not Yhorm), return to firelink.
Hey all. I've been trying to figure out this quest given the confusing and overly wordy nature of the Second Outing on this wiki.

I found something on Reddit that gave a clear answer for those who just want to save him, regardless of who does it. Siegward or Patches.

Their way to do it was thus: Give Siegward his armor. Don't kill the Old Demon King. (Not necessary I believe but it was how he suggests) This will lock out Patches from saving him. Enter Irithyll of the Boreal Valley, reach the bonfire by the bridge, light it sit whatever. Just reach that point so Greirat will talk about it. Send him off. Reload the area so he vanishes. Kill the Old Demon King. Go back to Firelink and he should be back and he'll mention being saved by Siegward.

I just did it myself so I can confirm. The furthest into Irithyll I got was the church with Anri inside and I went no further. I didn't attempt to even go near the moat till I did the quest. I beat the ODK but I believe just any boss will do. I also beat the ODK with the Great Swamp summon NPC so there's no clash there.

Hope this helps.
TIP: After you cross Irithyll bridge then talk to Greirat to send him on his second outing you can get him to return pretty much instantly if you kept Curse-Rotted Greatwood alive.

Just make sure he leaves the Shrine, and make sure you've done the prerequisites to make sure he returns alive. Giving Siegward his armour OR not buying it and telling Patches where Greirat went.

This saves me loads of time because I find the Demon king hard, and it's easy to let him die if you travel to certain areas.
I sent greirat to irithyll and told patches (he still had the armor). I confirmed both left and then killed old demon king but when i went back to firelink greirat wasnt there but patches had returned. RIP greirat
Forgot I wanted him to live, left Siegward sleeping, proceeded into Irithyll Dungeon and through to Dragons Peak. Came back through Irithyll, sent out Greirat, slayed the Pontiff, went to the kitchens and smacked Siegward by accident, he went back to sleep. I then found Dung-Covered ashes and thought Greirat had died only to find him returned on my next visit to the Shrine.
Well I just ruined my faith build playthrough. I talked to siegward before sending Greirat big sad face at not getting those lightning urns
remarkable how easy it is to **** up this questline
i did everything it says to doom greirat and he got doomed indeed (CONFIRMED)
Has anyone tried killing lothric and clearing the castle before letting him out? Will he still try to raid the castle later and when he does will that make him survive?
Just to point out to everyone: If greirat died in the boreal valley and you gave your ashes to the sanctuary handmaiden, from some point in the game the sanctuary handmaid WILL SELL ITEMS THAT GREIRAT WOULD SELL IF IT WERE GOING OUT TO THE LOTHRIC CASTLE. In my gameplay I was able to buy the lothric knight greatsword from the sanctuary handmaiden even though Greirat died in the boreal valley.

I just can't tell which event in the game made her sell the items (maybe cleaning up the lothric castle). My version of the game is the one that has both DLC's. If possible I would update this page asking for confirmation from players about this event but this wiki does not seem to allow it.