The details I can remember are small, but I do re-call that Tony is trying to get Loki to see that being mortal is not a life sentence of doom and they end up at a park. Loki was sitting on a park bench, while Tony went to get him a hot dog, when someone sits next to him on the bench. There is a misunderstanding involving the idea that a hotdog is made from real dogs and the stranger attacks; it turns out that the stranger is a relative of Loki's.
I have no idea who the author is and my searches on AO3 aren't working. I hope this rings a bell for someone.
EDIT: It's Shades of Grey by kuhekabir
Found by jheen