Before we start with some xrandr testing, have you tried using the FN+F5 button to swtich between the specific screens?
As the xrandr command shows, both screens are "connected". LibreELEC isn't made for multi-monitor environments.
So please, first try to use the FN-button combination (whatever it is, it might be different from FN+F5...a photo of the keyboard made by you could help in that regard), which is probably FN-F5 to switch the connecte monitors. Probably you have to press that combination multiple times as it switches from:
- internal + external monitor "mirrored" (means both screens will show the same)
- internal + external monitor "extended" (means that the laptop-screen will be extended to the connected monitor)
- internal only
- external only
probably not in that order 
if that fails or doesn't result in anything useful, you could try to manually turn off the LVDS1 screen (which is your internal laptop screen) by entering the following command:
xrand --output LVDS1 --off
Then the only connected screen should be the VGA1 which is your external screen.
You probably need to restart Kodi after that. So simply execute: systemctl restart kodi
Please do not reboot to restart Kodi as that would probably result that both monitors are connected again.