To wash the taste out of my mouth, I made a limeade in my kitchen. The combination of lime and ice and water was like my mouth walked into the freezer aisle of a grocery store on a 90-degree day. It was bracingly refreshing -- and not at all the feeling I got from eating the cookie.
If you want an Oreo that tastes like something other than an Oreo, I'd say pass on the Limeade and see if you can find a box of those Reese's. If you need those sweet, sweet limeade flavors, find some limes and get to squeezin'.
Lee Breslouer writes about food and drink for Thrillist, and he would be open to Lemonade Oreos. Follow him at @LeeBreslouer, because you can't make up a name that good.