Lockett, who has frequently clashed with MacKenzie over the wording, preparation and release of legal documents related to the city's current restructuring, said Friday that the vote would serve as "a wake-up call" for the city's top lawyer.
In February, Lockett went against MacKenzie's advice and released MacKenzie's legal opinion on the restructuring to the public.
The opinion, which held that the process being used was legal under state and local laws, was later countered by a conflicting opinion issued by the state Office of Legislative Counsel.
MacKenzie was promoted to general counsel in May 2010 to replace Chiquita Johnson, who resigned under pressure the January before in exchange for a severance package.
MacKenzie was hired four months before Johnson in 2007 and earns $136,359 to oversee the office of eight full-time employees.
Lockett placed the item on the agenda for Tuesday's regular commission meeting.