And the United Party for National Development (UPND) and Heritage Party leader Brigadier General Godfrey Miyanda have also applied to be joined to the case.
UPND Secretary General Steven Katuka made the application on behalf of the party.
In January, President Lungu declared that he is constitutionally eligible to stand in the 2021 general elections.
I am eligible to stand, if you want, go to Constitutional Court and they will tell you I am eligible to stand in 2021 and God willing and if people allow I will stand, President Lungu declared on arrival in Kalulushi.
The four political party leaders who petitioned the Constitutional Court are Danny Pule of the Christian Democratic Party (CDP), Wright Musoma of Zambia Republican Party (ZRP), Pastor Peter Chanda of New Congress Party (NCP) and Robert Mwanza from the Citizens Democratic Party (CDP).
They are being represented by lawyers Sakwiba Sikota, Milimo Lungu, Robson Malipenga and Bonaventure Mutale.
When the matter came up in chambers this morning, Judge Professor Margaret Munalula adjourned the case to February 27th for ruling on the applications made by LAZ, the UPND and Heritage party.