I gave it a try and didn’t notice any glaring issues as-is: The battlers seem to appear correctly behind the menu and the battle didn’t proceed until the menu was closed. The battle also didn’t restart, as far as I could tell.
The battler sprites flicker for one frame when entering or exiting the menu. I think this is a general issue with Scene_Battle, as I can see it even without Live Menu enabled when exiting the custom menu (if I slow down the frame rate to make it more noticeable).
I’ll see if I can make the Scene_Battle load the current battler sprites once right when it starts, which in theory should fix this in general. That could cause a slight (likely unnoticeable) delay when entering battle otherwise, though, so I’ll make it optional.
You should otherwise be able to use the plugins together without issue already, but do let me know if you notice anything else!