Lankhorst was born in a Roman Catholic family. He attended a protestant-Christian special schools in Meppel and Deventer, and the Roman Catholic Geert Groote College in Deventer. He started to attended gymnasium but later went to the HBS. He graduated in 1966. He continued to study political science at the University of Amsterdam and befriended his colleague Hans Janmaat. Lankhorst graduated in 1974 on a thesis on the Third Way.
Lankhorst joined the Political Party Radicals and entered the Amsterdam city council. He was originally candidate-alderman for education, but Roel van Duijn took this position for the PPR. Lankhorst left the council in 1980. A month later he became civil servant for the municipal department for Youth and Education. After the 1981 election Lankhorst became MP for the PPR. He was spokesperson on housing, education, transport and water management and youth welfare. He was one of the first MPs to be openly homosexual during his term in parliament.
After the 1982 election his former friend Janmaat became MP for the far right Centre Party. Lankhorst tried to avoid Janmaat as far as possible. In 1989 Lankhorst initiated a law to oblige high schools to have a statute which lays down the rights of students. In 1993 it was adopted. In 1991 the PPR merged with the communist Communist Party of the Netherlands, the left-socialist Pacifist Socialist Party and the progressive-Christian Evangelical People's Party. Lankhorst continued his membership of the Tweede Kamer under the new formation. When Ria Beckers left the parliament in 1993 in order to make room for a new political leader, which would lead the party in the 1994 election, Lankhorst took over the position of chair of the parliamentary party ad interim. He would not stand for re-election in the 1994 election.
In 1994 Lankhorst became a Knight in the Order of the Dutch Lion. After leaving parliament Lankhorst became an alderman in the submunicipality Bos en Lommer in Amsterdam. He left the position 1998 to become an independent advisor on youth policy.