Assuming standard optics (lens elements that are spherical or pseudo-spherical, rotationally symmetric about the optical axis), and "standard" cameras (no beam-splitting, or mirrors in the optical path), there is nothing optically that will cause single-axis lateral reflection ghost images whether they be left-right, top-bottom, or even diagonally oriented. This is because lenses perform transformations for any set of orthogonal input axes (i.e., x and y axes). Both dimensions are transformed: left is swapped for right, and top is swapped for bottom (in addition to scaling, and probably some degree of distortion as well). In linear algebra, swapping x for –x and y for –y is mathematically equivalent to a 180° rotation about the z-axis (that is, about the optical axis of the lens). Thus, in optically-generated ghost images (again, with "standard" optics), elements of the ghost are all reflected through the center of the image, not merely across a vertical or horizontal "fold line".
Stepping away from standard optics, cylindrical-sector lens elements, which curve in one dimension (usually laterally) but not in the orthogonal (vertical) dimension, could cause left-right symmetric ghost patterns. Anamorphic lenses, or at least current day anamorphic filters and adapters, come to mind. They compress the lateral field of view of a taking lens, which when printed or processed allows for much wider lateral fields of view than the camera is normally capable of. This is often used to film wide screen cinema.
Besides optics, I suppose it's possible that some sensor technologies could be susceptible to lateral "ghost images", perhaps due to how the sensor data is read or scanned. But that would be pure speculation on my part.
The last thing I can think of, at least within the optics or the camera itself, is some sort of reflection of the image from the sensor, back to some plane in the optical path (such as a filter plate or something behind the lens, fairly close to the film/sensor plane), and then back to the sensor. But in order for the reflected image to appear even somewhat in focus, the added reflection path must be fairly short compared to the back focus distance of the lens. That implies that the lens is focused extremely closely to the subject, and there would be quite a bit of distance from the exit pupil of the lens to the sensor. Furthermore, that reflection surface would have to be concave (looking from the face of the lens) in the lateral dimension only. Frankly, this last possibility is even more speculative and unlikely than the previous paragraph.
Outside of the camera, the most obvious explanation is a reflection through a window, automotive glass, or other largely transparent but semi-reflective surface. That would explain the same degree of magnification and in-focus reflected object as the real object in the image.