Forbes' lawsuit says he was passed over for promotion because of complaints he had made about discrimination in the department.
The lawsuit also accuses Lopez and city officials disregarded Forbes' right to be free from illegal race discrimination in the workplace.
Lopez said he could not talk about the lawsuit. City Attorney Patrick Baker also said he could not talk about the lawsuit.
"We'll respond to the allegations and look forward to defending the city in this matter," Baker said.
The suit comes after a discrimination complaint Forbes filed with the federal Equal Employment Opportunity Commission last August. That complaint charged discrimination on the basis of race.
After the federal investigation, the Justice Department indicated earlier this year it would not pursue the case itself.
The lawsuit says Lopez promoted a white lieutenant to captain over a black female lieutenant who was at the top of the rating list for promotion.
The lawsuit also says Forbes was passed over for promotion to a deputy chief position at least twice, including at least once where he was the top-rated candidate.
Forbes' suit requests a jury trial and asks that the defendants be assessed punitive damages "exceeding $10,000," and his attorney's fees and other costs.
The city has 30 days to respond to the lawsuit.