The up–down orientation unquestionably comes from the near-universality of light sources being above you. You'll notice that intense up-lighting is almost never found in the natural or artificial world.
(It's true that upwards-firing lights are often used in interior decoration, but these are almost always to illuminate walls and ceilings above us which then bounce light down to the contents of a room. Also, some techniques in photographic and studio lighting do use some up-firing lights, but these act as shadow fill, never as the primary light source—except when an unusual look is intended.)
To the extent that we expect a certain left–right orientation, this will almost certainly be predominantly a matter of consistency with prior graphical user interfaces. The near-universal standard of a top/left lighting metaphor goes at least as far back as the original Apple Lisa/Macintosh which cast its 1-bit, 1 pixel shadows to the bottom/right.
The fact that people of near-identical cultures can natively integrate either left-hand driving or right-hand driving suggests to me that there's no inherent reason why it needed to be one way or the other. Had the first interfaces begun with a top/right lighting metaphor, we'd probably be all as native to that as British people are with right-hand-drive vehicles.