They had mics on their lapels and that requires a little power box doesn’t it? At least my preacher’s does. I think that’s what this is.
Yes
Then why have microphones at the lecterns?
Portable lavaliers do indeed take a power box / transmitter. But she woul dot put that in the small of her back. She;d pocket it, and no wire would run down the middle of her back either, it would run from the microphone to the transmitter, in a side pocket or similar. The transmitter/battery packs have a spring clip too. I usually hang it on my belt.