It appears that In-N-Out
only operates in CA, NV, and AZ. And, aside from their "secret sauce", it's like jkath said - it's the quality and freshness of their ingredients that make them so special, "... we use only the freshest ingredients, delivered to our stores every day. Never frozen. And no burger hits the grill until you ask for it.
You might try contacting them via their website
and see if you can buy some of their sauce - then taste and test - and play "reverse engineering" food chemist. It seems a LOT of "Thousand Island" based burger sauces were born on the West coast.
The sauce recipes I would love to get my hands on are from "The Pig Stand" (the first drive-in in America) and Goff's Hamburgers (also another Dallas, TX creation).