People in Jackson say such labels are overstated.
"I've not seen any evidence of the radical side," says former Mayor Kane Ditto. "I've not heard any proposals that I thought were not in the mainstream."
Nonetheless, Lumumba -- who won Tuesday's general election -- has made it clear he intends to take the city in a liberal direction. He ran on a program of inclusive growth, and his mayoralty may offer striking evidence of a nationwide trend: strongly progressive policies being pushed in big cities, even in deep red states.
"He is a pretty progressive-minded person," says Councilman De'Keither Stamps.
In strongly Democratic Jackson, there was no doubt Lumumba would be elected once he won the primary. On Tuesday, he garnered 93 percent of the vote.
His performance in the primary had been stronger than expected. He avoided a runoff by taking 55 percent of the vote, easily coming out on top of a large field that included state Sen. John Hohrn and Hinds County Supervisor Robert Graham.
By contrast, incumbent Mayor Tony Yarber, who has been embroiled in sexual harassment lawsuits, took just 5 percent of the vote.
Yarber had defeated Lumumba in a special election in 2014, which was held to replace Lumumba's father, also named Chokwe. The senior Lumumba died just eight months after taking office. At the time, Yarber benefited from support from the business community. But the city clearly soured on him during his tenure.
"A lot of people looked and said we should have gone with Lumumba last time because the incumbent is terrible," says Bill Dilday, a political strategist in Jackson.
The first Mayor Lumumba had, in fact, a radical past. He was a leader in organizations that favored a separate African-American homeland within the U.S. or promoted other ideas for black self-determination.
"The father was a radical activist at one time," says Dilday. "Some people have never taken that label off of him. They've also put it on his son just because of that name. Those of us who've known him for a long time see him as squeaky clean."
The younger Lumumba said his parents inculcated him with social-justice values.
"They felt that giving us the movement was as important as giving us food, shelter, water and education," he told the Washington Informer, an African-American newspaper, earlier this year.
Lumumba, who is 34, has worked as a defense attorney. He is likely to follow some of his father's policies, such as holding "people's assemblies" to solicit input for city programs as well as creation of a fund to promote black-owned businesses. One of the complaints against Yarber is that contracting on his watch has been too cozy.
"For years, citizens have complained that they haven't had the opportunity to sit at the table and be part of the bidding process," says Debra Ellis, a spokeswoman for the Lumumba campaign. "Whether you're black, white, female, male, it doesn't matter. He wants to include all businesses and not just a small group of individuals."
Lumumba's most important task will be trying to improve the city's finances. Due to shortfalls and employee furloughs, city offices have been closed many days over the past couple of years.
"The first order of business for the new mayor is to get the basics right," says Ditto. "We have not had a comprehensive approach to basic city issues like infrastructure and policing and neighborhoods."
Paying for potholes and police will cost money. Lumumba wants to do it by securitizing future proceeds from a 1-cent sales tax hike approved by voters in 2014, in effect collecting a bigger lump sum up front. He has talked more vaguely about other potential revenue increases.
The new mayor will seek to increase the city's tax base over time by improving infrastructure and encouraging business development, but he'll be at pains to ensure that any economic gains are widely shared.
"People don't want to be another Detroit, or anything like that," says Councilman Stamps. "But we have to navigate those waters in an equitable way. People want to be involved in the prosperity of the community they live in."
Among the immediate beneficiaries of Lumumba's election will be city workers. A public employee union was among his top donors, and he's talked not only about ending furloughs but offering raises.
"He believes in moving away from what has been a national trend -- not only in city government but state government -- of privatizing out a lot of government services," says Brenda Scott, president of the Mississippi Alliance of State Employees, which has a collective bargaining agreement with the city. "He's going to be looking at ways our city employees can perform a lot of duties."
Lumumba's ideas may or may not be fairly described as radical, but he'll certainly favor an activist-government approach.
"We know exactly what we're going to get if we stay on the traditional course of government," says Councilman Stamps, "especially in Mississippi."
