Early and personal life
Strømsted was born in Kristiania, as the daughter of storekeeper Jørgen Andreas Strømsted and Signe Beatrice Hansen. She was married to actor Jens Bolling from 1945 to 1952, and to physician Ivar Dommersnes from 1968 until his death in 1994. She was also in a secret relationship with Johan Borgen, as chronicled in her 2001 memoirs Alt har sin tid. 
Strømsted made her stage debut as "Helga" in Bjørnstjerne Bjørnson's play Geografi og kjærlighed at the National Theatre in Oslo in 1942, in the last production directed by Bjørnson's son Bjørn Bjørnson. She was employed at the National Theatre from 1941-45, and again from 1949.
During the German occupation of Norway the situation at the theatres was characterized by severe nazification attempts from the authorities, and boycott from the public. Strømsted joined the group of actors that started underground meetings where they secretly studied Stanislavski's system. The result of these undercover meetings was the founding of the theatre Studioteatret in 1945. She played for Studioteatret from 1945 to 1949. Among her roles were "Emily" in an adaption of Thornton Wilder's play Our Town, "Polly" in Weill and Brecht's The Beggar's Opera, and "Natasja" in Anton Chekhov's A Marriage Proposal.
Strømsted has interpreted several roles from Henrik Ibsen's plays. One of her most important roles has been "Nora" in A Doll's House, which she played at Rogaland Teater in 1950, for Radioteatret in 1953, for Riksteatret in 1956, and at the National Theatre in 1957. She acted in the films Andrine og Kjell from 1951, and Blodveien from 1955. She has participated in nearly 100 productions for Radioteatret.
From 1965 Dommersnes initiated a career as a reciter of poetry, performing all over Scandinavia, either alone or with musicians. Several of her performances have been broadcast by radio or television. She wrote an autobiography, Alt har sin tid, in 2001. She was honorary member of Kunstnerforeningen from 1975, and of the Norwegian Actors' Equity Association from 1999, and has received several prizes, including Oslo City's Artist's award in 1985, Herman Wildenvey's Poetry Prize in 1999, and the honorary prize of the Norwegian Broadcasting Corporation's Radioteatret in 2001.  She was a member of the Norwegian Academy for Language and Literature.
In 2000 she was decorated as a Knight, First Class of the Order of St. Olav.
She died on 6 April 2014, aged 91.
- Mürer, Annette. "Liv Dommersnes". In Helle, Knut. Norsk biografisk leksikon (in Norwegian). Oslo: Kunnskapsforlaget. Retrieved 24 April 2009.
- "Liv Dommersnes er død" (in Norwegian News Agency). 7 April 2014.
- Rønneberg, Anton (1949). Nationaltheatret gjennom femti år (in Norwegian). Oslo: Gyldendal. pp. 389–406.
- Olsen, Arne Thomas; Else Martinsen (1995). Studioteatret. Frihet og fornyelse (in Norwegian). Oslo: Universitetsforlaget. ISBN 82-00-22366-3.
- "Det Norske Akademi for Sprog og Litteratur" (in Norwegian). Norwegian Academy for Language and Literature. Retrieved 25 April 2009.