The achievement title is a reference to the video game Portal. Its antagonist supercomputer GLaDOS offers the player cake as an incentive for solving a series of puzzles; however, no cake is ever rewarded. The achievement refers the wall graffiti in-game stating THE CAKE IS A LIE which has become a popular internet meme.
Strangely the cake doesn't need any chocolate to be cooked. The Chocolate is a Lie.