Lucas was born in Kansas City, Missouri, the son of Quincy Bennett Johnson. His mother describes his childhood as one of living in two worlds. He earned a scholarship to attend The Barstow School, a private school far removed from the harsh economic realities of Kansas City's east side. "He saw we were struggling," Johnson says. "One time we lived in a hotel, and it was horrible. Quinton would go in the bathroom to study." Determined to overcome poverty, Lucas devoted himself to school, dedicating himself to academics and sports. He became one of the Barstow School's most exceptional athletes, was elected student body president twice, and was one of the top students in his class, but he experienced a conflict of identity as the hopes of his mentors and his ambitions pushed him further from his roots. In this time he found himself forming lifelong relationships with the school's janitors and felt reluctant about leaving Kansas City upon graduation. Encouraged by his college counselor, Lucas accepted an offer to study at Washington University. Lucas found his niche in political science and studied abroad in South Africa. Living in Cape Town, he closely studied the politics and culture of apartheid. This experience challenged Lucas' assumptions about inequality but more importantly shaped the way Lucas would approach democracy, consensus-building, and relationships in extremely divided environments. He attended law school at Cornell, where he was encouraged by a professor to assist in Curtis Osborne's appeal for clemency. Though the appeal failed, Lucas found the legal experience to be transformative.
In 2015, Lucas won a city council seat representing the Third-District-at-Large, gaining more than 70% of the vote. His message was concerned with bridging the gaps between east and west in a divided city. When asked what was the greatest challenge facing Kansas City, Lucas said, "How do we get people from jobs in my part of the city, the east side of Kansas City, off into other parts of the city or even to Kansas?" Housing policy became a primary focus once Lucas was situated on City Council. His housing policy aimed to ensure housing availability for Kansas City families is geared toward the symmetrical development of new housing supply along with the renovation of existing properties. Lucas played a decisive role in shaping a 2018 ordinance that defined affordable rent as equaling 30% or less of the city's median income, what was then $1,100 a month. In an interview with the Kansas City Business Journal, Lucas explained that while he realized "that $1,000 a month is still pretty high for a lot of people, but what we’re trying to do is say that we will not give incentives based on affordability standards for units that are north of that figure.” He is currently Chair of the City Council Housing Committee. Quinton also serves on committees related to Planning, Zoning, and Economic Development; the Airport; Transportation and Infrastructure; Neighborhoods and Public Safety. During discussions surrounding the finance and development of a new airport in August 2017, Quinton Lucas emerged as a firm advocate for transparency, disagreeing with Mayor Sly James. “My concern is I continue to believe we overuse closed sessions,” Quinton Lucas, told The Kansas City Star. “I think the spirit of the Sunshine Law is not for council to deliberate on myriad issues on public policy in secret.” In January 2018 Lucas proposed a five point targeted strategy for reducing crime: fund social workers in each police patrol division, deploy officers to economically distressed areas and not just entertainment districts, recruit diverse candidates for the police force, challenge the necessity of incarcerating citizens for municipal offenses, and appeal to the state of Missouri to adequately fund Kansas City's criminal justice system to lighten the load of public defender cases and improve overall pay. In October 2018 police in Lawrence, Kansas "got a call of an unconscious man at 8th and Massachusetts. found Lucas asleep in his car." He "was booked for misdemeanor driving under the influence of alcohol or drugs... and released on a $750 bond", even though he was reportedly asleep, not driving. In the 2019 mayoral election, Lucas was elected Mayor of Kansas City, Missouri after receiving approximately 59% of the vote.