Because I use my cell phone for internet connection I need to know if sharing files between my phone and my computer or iPad uses that connection. It gets expensive to use that connection and I need to watch it -- and limit my use. So far I haven't found any info about how Lightroom uses the net.
Yes, it does, though there is an option to sync only over wifi.
As John says, there's an option to avoid using cellular data - just tap the Lr logo in the upper left and you'll see it there:
Note that you can turn it off and on at will, so if you need to sync "just this once" you can disable it temporarily (don't forget to turn it back on when you're done!)