Short answers, pulled from the story.
The Lucas critique refers to Robert Lucas's 1976 article arguing that existing large-scale macroeconometric models lacked structural validity for predicting new policies. This work marked a representative paradigm shift in macroeconomic theory during the 1970s.
Ragnar Frisch published a paper in 1938 containing the core logic of what would later become known as the Lucas critique. Trygve Haavelmo discussed similar arguments in his work from the 2nd of May 1944, laying out early economic principles about policy changes and data reliability.
Historical negative correlation between inflation and unemployment known as the Phillips curve could break down if monetary authorities attempted to exploit it. Permanently raising inflation caused firms' inflation forecasts to rise, which altered employment decisions made by businesses across the economy until the trade-off disappeared once agents adapted their forecasting mechanisms.
Parameters inside these models shifted systematically whenever policymakers altered the rules of the game. Changing policy alters the very structure of the econometric model used to evaluate it because decision rules within Keynesian models cannot be considered structural if they change with government policy variables.
Statistical analysis using high-level aggregated data regarding Fort Knox indicated that robbery probability was independent of resources spent on guards. This conclusion ignored the fact that criminals' incentives depend directly on the presence of guards, meaning a change in security policy would lead criminals to reappraise costs and benefits of robbing the facility.