Keith-Lucas was born in Hastings, East Sussex in 1982. She is the daughter of Christopher Leslie Keith-Lucas (born 1949) and Claire Forrester. Her middle name comes from her grandmother Dorothy de Bauduy Robertson, who was killed in a road accident in 1979; Dorothy's husband was David Keith-Lucas, who was an aerodynamicist in Kent during World War II, and President, from 1968–69, of the Royal Aeronautical Society. Sarah has an older brother.
Keith-Lucas joined the Met Office in 2007 and started presenting forecasts for BBC Weather in 2008. She has done the five-day weather forecast on the BBC One series Countryfile. She also presents occasional weather-based documentaries on the BBC News and BBC World News channels Climate Check and Weather World, which she co-presents with Nick Miller, and once included an item for children about making a rain gauge she presented along with her son Oscar.