The group said the support Mr Lawan is currently getting from chieftains of the All Progressives Congress (APC) is in secret pursuit of personal ambitions ahead of 2023.
Mr Lawan is expected to be in contest with Ali Ndume, a former Senate Leader on Tuesday for the position.
In a statement by Yerima Shettima, the organisation identified APC leader, Bola Tinubu, and Nasir El-Rufai, the governor of Kaduna State, as people behind Mr Lawan.
“We advise the Tinubus and Elrufais of this world to shove aside any desperate move on 2023 and allow a level-playing field for all political offices.
“No one should hide behind any political party to turn Nigerians into mere manipulable pawn. That will be undemocratic imposition and totally unacceptable,” the statement quoted Mr Shettima as saying.
The group said it predicted that Senator Danjuma Goje would step down when he is pressured into submission for his pending case at the Economic and Financial Crimes Commission (EFCC).
AYCF said recent development has vindicated its prediction.
“We also declared that he could alternatively be forced to step down from the race in exchange for his freedom from EFCC’s hot chase.”
The EFCC withdrew from Mr Goje’s corruption trial on Friday, saying it did so at the request of the office of the Attorney General of the Federation.
“We are happy to inform all Nigerian progressives that we have been vindicated in all the public declarations we made recently on the contentious seat of the Senate presidency.
“It is obvious that the desperation to make the road to Senate presidency smooth for Tinubu’s acolyte (Sen Lawan), Buhari’s foot-soldiers, especially Governor Nasir El-Rufai are coming up with a new narrative to pull a blind wool over our eyes.”
The group declared support for Mr Lawan’s opponent, Mr Ndume.
“We see the desperation in the use on intimidation of senators to fall into the booby trap. Let the world know that we, in the AYCF are watching very closely and we will democratically resist this imposition in broad daylight.
“It is now abundantly clear that only Senator Ali Ndume is capable of preserving the independence of the Senate under the Next Level mantra,” the statement reads further.