He said that Atiku's goal wouldn't work because it would mean switching from one Muslim Fulani president to another Muslim Fulani president.
Lawal was responding to rumours that he had stopped working for Peter Obi, the presidential candidate of the Labour Party, and started working for Atiku.
"I will always be a Peter Obi fan," he said, and he warned that if Atiku got his way, Obi would be a symbol of one ethnic group being more powerful than others.
Lawal said in a statement that he still backs Obi.
Part of the statement said, "I just heard on the news that I quit Peter Obi to work for Atiku Abubakar. Nothing could be further from the truth than this. Since it started, I've never thought about joining the PDP because I see it as the worst kind of group of oligarchs and reactionaries.
"Also, every year I have to fight Fulani herdsmen who want their animals to come into my farms and eat my crops.
"This is in addition to the fact that they want to take over the family farms of my relatives, as they do everywhere in the North. All of these things are done without care, while their elite relatives who are in charge of the government stay quiet.
"Also, I think it's the worst kind of Muslim-Muslim ticket for one Muslim Fulani President to hand over power to another Muslim Fulani President." It also means that one ethnic group is stronger than others. I remain a Peter Obi devotee. "Anything that says otherwise is fake news."