Protesters chanted anti-government songs at the Unity Fountain during the demonstration.
They also sang the national anthem and demanded that police brutality be ended.
The protest was held in a secure environment.
Sowore had previously stated in a statement that the planned protests would take place on October 20th.
Only indoor and virtual protests would be permitted on Wednesday, according to the police.
"Our attention has been drawn to the most recent statement attributed to the Lagos State Command of the Nigeria Police to the effect that no "street protests" will be allowed tomorrow (Wednesday) to commemorate the historic #Endsars rebellion of 2020 and its attendant fallout due to police repression and the Nigerian army's murderous intervention," Sowore said.
"We state unequivocally that the Nigerian police do not have the authority to prevent citizens from participating in street protests; the right to protest unjust policies, tyranny, and oppression is an inalienable right, and as such, these latest claims are at best superfluous and belligerently arrogant."
"We implore the police authorities to ensure that they carry out their responsibilities in protecting protesters who will be on the streets tomorrow in cars, bicycles, tricycles, skateboards, and on foot throughout Lagos and its environs" (Wednesday).
"If anything, untoward happens to any Nigerian citizen engaged in lawful protest during the #Endsars anniversary, the Lagos state police commissioner will be personally held liable."