Short answers, pulled from the story.
The Lucas critique argues that it is naive to predict the effects of a change in economic policy purely from relationships observed in historical data, especially highly aggregated data. It states that the decision rules of Keynesian models, such as the consumption function, are not invariant to changes in government policy.
The Lucas critique is named after Robert Lucas, an American economist, based on his work on macroeconomic policymaking.
Robert Lucas presented the critique in a 1976 paper, though the underlying argument was not new at the time. Similar reasoning had already appeared in the work of Frisch in 1938 and Haavelmo in 1944.
The Fort Knox example notes that Fort Knox has never been robbed, so aggregated data would suggest guard spending has no effect on robbery risk. The critique argues this conclusion is misleading because it ignores how criminals would respond if the guards were removed.
No, the Lucas critique does not invalidate the idea that fiscal policy may be countercyclical, an idea some associate with John Maynard Keynes.
Kydland and Prescott published "Rules rather than Discretion: The Inconsistency of Optimal Plans" shortly after Lucas's article, describing how short-term policy benefits can be negated by shifting expectations and how time consistency could overcome that. Their work, and the research it inspired, opened a research program in dynamic, quantitative economics.