Preheat oven to 325 degrees F. Butter and lightly sugar four 6-ounce ramekins. Using the paddle attachment on a kitchen stand mixer, beat yolks, buttermilk, lime zest, and lime juice on medium speed until well combined. Reduce the speed to low and slowly add flour, the 2/3 cup sugar, and the salt, until just combined. Transfer to another large bowl. Thoroughly wash mixing bowl with soap and hot water; return to stand mixer. Using the whisk attachment, beat egg whites in the clean bowl until stiff peaks form. Gently fold the beaten egg whites into the yolk mixture, a little at a time.

Divide mixture evenly among ramekins. Place ramekins in a roasting pan and fill the pan with hot water halfway up the sides of the ramekins. Bake about 1 hour, until the top springs back when gently pressed and the cakes have a light golden color. Remove ramekins from water; allow to cool slightly. Carefully invert each onto a plate.