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.
4818, I have many times put them in the back like that and run it up and over the shoulder to keep from exposed wires coming out of the jacket pocket.
The video before the debate started showed Lester Holt messing with his on his lower back.