Liya Qajar (Kadzhar) a descendent of the Persian royal dynasty, was born in Baku, Azerbaijan, in 1927 to engineer Sultan Uveis Mirza Qajar (the son of military commander Ali Qulu Mirza Qajar) and his wife, a Georgian teacher Tamara Dzidzikashvili. Liya Qajar’s brother, physicist Çingiz Oveys oğlu Qacar, became an academician of Azerbaijan Academy of Sciences. Qajar studied architecture at the Academy of the Arts in Leningrad. There, she married her classmate, Syarhey Musinky (who later became an academician of Belarusian Academy of Architecture); the family would have three children. Upon graduating in 1952, the couple moved to Minsk. 

Qajar first worked at Beldzyarzhpraekt, remaining there until 1959. At this time, she designed Belarus sanatorium in Sochi, Russia (1954-1959, with Musinsky), the memorial to the victims of fascism in Trostyanets (1958), and residential building with commercial spaces on Lenin avenue (1958). 

Between 1962 and 1966 Qajar worked at Minskpraekt. Among Qajar’s individual designs of the period are a residential building on Leningrad avenue (1960), a complex of residential and commercial buildings on Apansky street (1964), a complex of residential buildings with retail spaces on Respublikanskaya street (1965), dormitory on Karalya street (1966). With Musinsky, she worked on the design of the Textile Factory Palace of Culture (1962-1965). Qajar was also the winner (with Musinsky and Dmitry Kudryavtsev, the husband of Askana Tkachuk) of internal Minskpraekt competition for the redevelopment of Nyamiga neighborhood in Minsk; the bold project was approved for construction in 1972, but as the construction works began it became clear that it was too challenging for Belarusian construction industry and economics, and the project was stopped. 

Later in her life, Qajar turned to interior design and subsequently pedagogy. Between 1967 and 1976 Qajar taught interior design at Belarusian State Institute of Theater and the Arts. At this time, she also worked as an artist at the Minsk Art Production Combine of the Art Fund of the BSSR. Among her designs of this period are memorial park Vyazynka (Belarus, 1973; team member), and the interiors of restaurants and reception areas in hotels Matel and Planeta in Minsk (1982).