Lisbeth Beate Lindenskov Petersen (born February 28, 1939) is a former Faroese politician in the Faroese Union Party. She was one of the first women to reach a top position in Faroese politics. Petersen served as mayor of the capital, Tórshavn, from 1992 to 1996 and was the first female mayor of Tórshavn. She was a member of the Faroese Parliament from 1990 to 2008, she was the first Faroese woman who was elected to the Danish Parliament, she was a member of the Danish Parliament from 2001 to 2005. From 2001 to 2004 she was parliamentary leader and head of her party.