Lien was born in 1918 in Ho Chi Minh City into an intellectual family. Her father was Thai Van Lan, one of the first Vietnamese electrical engineer graduating in France.
She started playing the piano when she was four. At the age of 100, she still played music every day.
In 1946, Lien studied in France. She got married to Tran Ngoc Danh, who was then head of the permanent delegation of the Democratic Republic of Vietnam. After that she and her husband returned to Vietnam and joined the resistance against the French colonialists. She and Danh had two children - Tran Thu Ha and Tran Thanh Binh. After Danh passed away, Lien got married to her second husband Dang Dinh Hung with whom she had a son - Dang Thai Son.
Lien was among the founders of the Vietnam Music School (now the Vietnam National Academy of Music) and headed the Piano Department until she retired in 1977.
Lien was also one of the first Vietnamese female pianists and compiled the first piano curricula in Vietnam.
Two of her children also became great artists. People’s Artists Tran Thu Ha was head of the Vietnam National Academy of Music and People's Artist Dang Thai Son was the first Asian pianist to win the first prize at the 10th International Chopin Piano Competition in Warsaw in 1980.