Born in Klaksvik, Faroe Islands, Lützen trained at the Design School for Women (Tegne- og Kunstindustriskolen for Kvinder) in Copenhagen and studied under the graphic artist Povl Christensen.

[1] Lützen was best known for her black and white woodcut and linocut prints in which she portrayed Faroese nature and magical motifs.

[2] She showed her work at group exhibitions in Copenhagen, Reykjavík and Bergen and in 1980 participated in a traveling exhibition of Faroese artists presented in Denmark, Norway, Iceland, Scotland, and Finland.

[3] Several of Lützen's pieces are held by the Listasavn Føroya and the Vejle Museum of Art.

[4][5] Lützen created several designs for Faroese stamps based on fairy tales.