Beevers was born as Lizzie Johnson on 7 November 1884 in Skipton, England to cabinetmaker Spencer Johnson. Her mother died at a young age, and her father remarried in 1893.
Beevers married her husband, Harold William Beevers, in 1914. The couple had one son, Charles Spencer, that same year. She was widowed in 1943.
Beevers died in Ilkley, England on 7 August 1996 at the age of 111 years, 271 days. At the time of her death, only Lucy Askew was older than her in the United Kingdom. She was one of the top 20 oldest people to die in the country, and was survived by her son Charles, who died in 2004 aged 89.