Often the very noise you wish to remove is directly in the frequencies of human voice. The more you remove the noise, the more you screw up the voice.
Play with specific frequency dampening, but if it is general "white noise", you just supress it some and live with the result.
Also, sometimes a noise gate can deal with really low level noise.
fwiw- for the next series of lectures, get him to invest in good microphones and have them well placed in the room.
I often record talks in a room where the a/c noise is distracting. By good placement of mics I can reduce that crud to well below the irritation threashold...