Is it permissible for the Imam to hold the microphone with his hands during prayer to amplify his voice for the congregants, especially since a lapel microphone causes interference?

It is permissible for the Imam to carry a sound amplification device during prayer, because this is one of the light actions that do not affect the validity of the prayer, especially if it leads to a benefit such as his voice being heard. This is confirmed by what is stated in Kashshaf Al-Qina' regarding the permissibility of wearing a garment and a turban and wrapping it, and carrying something and putting it down, like the action of the Prophet, peace and blessings be upon him, when he carried Umamah or wrapped himself in his izar while in prayer.