Lui was raised by his grandparents on Niue after his parents and older siblings migrated to Wellington, New Zealand. His parents sent for him when he was nine years old and he attended Newtown School. Soon afterwards, he transferred to Naenae School in Lower Hutt when his parents took the tenancy of a State house there. Lui left Naenae school in 1950 to attend Wellington High School. On leaving school, he joined the New Zealand merchant navy, and was immediately caught up in the prolonged and acrimonious waterfront workers strike of 1951. He returned to Niue in 1956 to care for his grandparents and has lived there since. There, he was subjected to colonial discrimination which motivated him to political activity to change an oppressive, paternalistic system run by the New Zealand Government. He organised the first ever strike on Niue.
Following the death of Robert Rex in December 1992Young Vivian was elected Premier. At the following 1993 election Lui was re-elected to the Assembly, and on 12 March was elected Premier, defeating Vivian 11 votes to 9. In March 1994 Finance Minister Sani Lakatani resigned from Cabinet, but was reinstated by Lui in the leadup to a confidence vote. Lakatani subsequently resigned from Cabinet on 8 November after losing the finance portfolio in a cabinet reshuffle. He joined the opposition, which organised itself into the Niue People's Party and effectively deadlocked the assembly. A series of tied confidence votes followed, and the government was effectively unable to pass legislation through the Assembly for the rest of its term. An attempt to break the deadlock by declaring the seats of opposition MPs vacant was ultimately declared illegal by the Niue Court of Appeal. The 1996 election saw Lui win re-election in his seat, and he was narrowly re-elected as Premier, defeating Robert Rex, Jr by 11 votes to 9. Lui's second-term was more stable, and the government was able to pass anti-corruption laws and a ban on drift-net fishing in its Exclusive Economic Zone. It also partnered with Panamanian law firmMossack Fonseca to set up an "international business centre" providing shell companies to international clients, and established a free internet service with the Niue Internet Users Society. Lui lost his seat in the 1999 election, and announced his retirement. He was replaced as premier by Sani Lakatani.
