He did his secondary studies at Bolongo, Kisantu and Albert I College in Kinshasa, which he left in 1955. He went on to Louvain University in Belgium in 1958 and took a degree in Philology in 1961 and a Doctorate in Law in 1962, being specially mentioned “for the highest distinction”. He then went on to the faculty of law and economics at Paris where he got a diploma.
In January 1963, Lihau was hired to be professor and dean of the faculty of law at the University of Lovanium. For a time he lived on campus.
On 27 November 1963 President Kasa-Vubu announced the formation of a new "Constitutional Commission". The commission convened on 10 January 1964 in Luluabourg, with Lihau serving as its secretary. A draft was completed by 11 April and, after a political dispute between Kasa-Vubu's government and the commission, was submitted for ratification to the Congolese electorate at the end of June. The "Luluabourg Constitution" received 80% approval and was subsequently adopted.
In 1965 another period of government paralysis led Colonel Mobutu to seize total control of the country. He requested that Lihau draft a new constitution, which was adopted on 24 June 1967.
In 1968 Lihau was named president of the Supreme Court of Justice of the Congo. He assumed the position on 23 November. In 1971 he joined the executive committee of Mobutu's party, Mouvement Populaire de la Révolution (MPR). Three years later he was made a commissioner of its political bureau. However, in June 1975 he refused to support Mobutu's violations of the constitution. Lihau was subsequently dismissed from the Supreme Court, removed from his teaching position, and placed under house arrest. In 1982 he and 13 members of Parliament founded the Union pour la Démocratie et le Progrès Social (UDPS) as an opposition party to Mobutu, of which Lihau subsequently became president. In retaliation, Mobutu incarcerated him, suspended his rights, confiscated his personal property, and eventually banished him to the village of Yamake, Équateur Province.
By 1985 Lihau's health had deteriorated and he was granted political asylum in the United States, moving to Cambridge, Massachusetts. He subsequently became a professor of constitutional law at Harvard University. Using his professional background, in 1989 he founded a political conference with the goal of democratizing the Congo.
He died on 9 April 1999, seven days after the death of his wife. He was buried in Gombe, Kinshasa. Three of their daughters organized a mass of thanksgiving in their honor in Gombe on 28 March 2015. Several important politicians attended the ceremony, including Léon Kengo and José Endundo Bononge.
Reserved and rather uncommunicative, but with an excellent legal mind and a taste for delivering radical oratory at the ceremonies which mark the end of the lawyers’ holiday season. He is one of the few prominent Zaireans who has remained in a position of authority since independence.
Lihau married Sophie Kanza on 26 December 1964. They had six daughters: Elisabeth, Anne, Irene, Catherine, Rachel and Sophie. Due to his political activities and flight from persecution they spent most of their later lives separated.