In a large bowl, beat cream cheese with an electric mixer until light and fluffy, about 1 ½ - 2 minutes. Add the dry pudding mix and lime juice; mix until well combined. It will be very thick, which is fine! Gradually add the milk, mixing constantly, until the mixture is completely combined. It should look like a thick pudding at this point; a few little lumps are fine. Mix in the lime zest.
Gently fold in half of the Cool Whip, being careful not to stir too vigorously, which will deflate the light, airy texture.
Spread about ¼ cup of the pudding mixture in a very thin layer in the bottom of a deep 8-inch square dish. Add a layer of graham crackers, breaking the crackers as needed.
Spread ⅓ of the remaining pudding mixture on top of the graham crackers. Repeat with another layer of graham crackers, another layer of pudding, a final layer of graham crackers, and a final layer of pudding.
Spread the remaining half of the Cool Whip on top.
Freeze the icebox cake for at least 4 hours, or refrigerate overnight.
If frozen, allow the dish to sit on the counter for 15-20 minutes so that it softens slightly before you try to slice it. Garnish with optional toppings just before serving.