Derby is a city in Lucas County, Iowa, United States. The population was 90 at the time of the 2020 census. Derby was platted in 1872. Accord…Derby is a city in Lucas County, Iowa, United States. The population was 90 at the time of the 2020 census. Derby was platted in 1872. According to the United States Census Bureau, the city has a total area of 0.26 square miles, all land.