Paratext Lite lacks the a menu option to do this, but there is a shortcut key to do this
Ctrl + I - insert consultant note.
(while Ctrl + N - inserts normal notes)
Now if one has a external/bluetooth keyboard with Ctrl keys on then this is easy to do, but without that typing Ctrl's requires a non standard android virtual keyboard.
Ctrl + I will insert a new CN into the first selected enabled/(selected for viewing) CN project. (or if none selected the first available CN project on the device)