I am currently challenged by this issue regarding the close button which closes the lightbox from the desktop view but does not close from the mobile view.
I see the problem now,
On your desktop editor the button to close the Lightbox has the id ‘#Button1’.
On the mobile editor you manually added another button with the id ‘#MobileButton1’.
You have to remove the mobile button from the mobile editor and use the same button as for the desktop editor. Maybe is hidden behind the text. If you cannot find the button in the mobile editor you can use the Layers tool (Tools>Layers) to spot it. After this you can manually place it where you want on the mobile version.