As you were taking pictures using artificial light the most likely cause of your horizontal line is a small frequency difference between your live view sensor refresh rate and the local power-line frequency.

As you were using street lighting there would be a brief period, imperceptible to us, where the scene isn't illuminated - this would cause the band. As the street lighting isn't synchronised with your sensor, this band could appear at any point within your live view image - if it was synchronised the band would occur when the sensor refreshed and so would not be visible. Working on the assumption your sensor updates at 60Hz (a very precise 60Hz), if your local mains power-line frequency was off-spec at say 59.5Hz (which frequently happens as it's not referenced by a quartz crystal oscillator, unlike your camera) this would result in movement of the band.

A similar phenomenon can occasionally be seen in some film and TV programs where there is a CRT display in the scene with a slowly moving horizontal band. This is caused by the same things, a lack of synchronisation, and a minor frequency difference between the mains-powered CRT in the scene and the observing video camera.