Did a little research and came up with this (though I’ve never clipped any Lav mic pointing away from the mouth).
-If you don’t know the lecturers speaking habits and are in an uncontrolled environment. Or for example they do have a tendency to look down and exhale heavily through the nose or they are very active speakers constantly turning to extreme left/right, engaging all of the audience. Pointing it down and using a clip that creates a loop in the wire can help to eliminate many potential problems.
-If the speaker is very calm and rehearsed. They just look forward and speak in a clear tone. The environment is silent and controlled, then clip on the mic “so it looks nice on video” (with audio still in mind, of course).
In any case, be sure to record sound from another mic as well. If its a one camera shoot, the on-camera shotgun on CH1 and Lav on CH2 will at least give a fail safe in case there is a problem with the wireless. I generally prefer to place my wireless receiver close as close as possible to the speaker, like just off-stage and run XLR back to my setup. It might be preferable to run XLR and place the second mic on a stand closer to the speaker. Then you can mix the two in post to get a good “lecture hall” sound to your liking. As opposed to the dry quality of a lapel only, which I think feels very unnatural in this scenario.
*Edited my post, regardless of the type of mic, I’ve never placed it upside down pointing away from their mouth.