The President also vowed to weed out anyone found guilty or frustrating the anti-corruption war.
Buhari had on Monday, October 10, ordered the dismissal of the two top government officials over alleged corruption.
He directed the EFCC and the Independent Corrupt Practices and other related offence Commission (ICPC) to "proceed with investigation" involving Lawal and Oke.
In a statement released late Monday by the president's spokesman, Garba Shehu, Buhari vowed to weed out anyone found guilty or frustrating the anti-corruption war.
He said, "Those who ask the question of what next? The president has taken the administrative action; all other actions will be taken by relevant government agencies.
"When and where they (the agencies) have reasonable grounds to charge former or serving officers to court under our laws, they do not require the permission of the president to do so.
"The position of the president, therefore, is that investigation agencies that have already commenced the investigation of the two officers removed from office will go on with their work of investigation without any interference or hindrance.
"Based on his wish and desire for a strict observance of the law, the president expects the EFCC, ICPC and such agencies to proceed with ongoing investigations."
A presidential probe panel headed by Vice President Yemi Osinbajo had recommended the termination of Lawal and Oke's appointments.
Lawal was alleged to have violated due process in the award of contracts under the Presidential Initiative on the North East (PINE).
The panel probed Oke over the discovery of huge cash by the EFCC in a residential apartment at Osborne Towers, Ikoyi, Lagos, for which NIA laid claim to.