Radebe was born in the Diepkloof section of Soweto, near Johannesburg, as one of eleven children.
When he was 15 years old he was sent to the "bantustan" of Bophuthatswana by his parents in order to keep him away from the violence that was affecting Soweto during the apartheid era.
In order to keep himself busy during his stay in Bophuthatswana, Radebe played football (as a goalkeeper).
He was later spotted and signed by the Kaizer Chiefs Football Club as a midfielder. In 1991 he was shot while walking down the street, though he was not critically wounded.
The motive for the shooting never became clear, but Radebe himself believes that someone had been hired to shoot him in order to prevent him from moving to another club.
Radebe was first included in the South African national team in 1992. Partially motivated by the shooting incident, Lucas and another South African player, Philemon "Chippa" Masinga, moved to Leeds United in 1994; Radebe was sold by the Kaizer Chiefs for GBP 250,000.
In 1996, he was a member of the South African team that won the African Nations Cup. Radebe became a star player for Leeds and was nicknamed "The Chief" by its fans partly due to his previous club and partly his absolute rule in defence .
In recognition of his leadership and ability, Radebe was appointed captain of the team for the 1998/99 season. Radebe was also the captain of the South African national football team (nicknamed the Bafana Bafana) in the 1998 FIFA World Cup.
As captain of Leeds, Radebe was very successful: in the 1998/1999 season, Leeds finished fourth in the FA Premier League qualifying for the UEFA Cup. During the 1999/2000 season, Leeds finished third in the Premier League and qualified for the Champions League, reaching the semi-finals.
In 2000, Radebe sustained knee and ankle injuries, which kept him out of the game for almost two years.
After his recovery, he captained South Africa in the 2002 FIFA World Cup. Radebe has also been an ambassador of FIFA for SOS Children's Villages; he also received the FIFA Fair Play Award in December 2000 for his contribution in ridding soccer of racism as well as for his work with children in South Africa.
He was voted 54th in the Top 100 Great South Africans in 2004. At the end of the 2005 season, Radebe retired from professional football in a star-studded testimonial match at Elland Road involving players from all around the world, and Leeds United players past and present. He has been offered a role on the Leeds United coaching staff as a result.
The Leeds rock group The Kaiser Chiefs take their name from his former club. He is still a crowd favourite at Elland Road with the fans still singing his name even after his retirement showing how much he endeared himself to the fans during his playing career.
His shirt number (No.5) has remained unused in the two seasons following his retirement even though there has been no official club announcement on the retirement of the number in his honour.