That waveform looks pretty typical, actually.
If you were to zoom in much closer on the time axis, each "line" as you call it would become one (or more) peaks or troughs of the wave. As you probably know, the amplitude of these lobes represent the positive and negative variation in air pressure that transmits the sound. They are roughly centered around the central axis, but there is no need for them to be perfectly symmetrical. In fact, it's almost impossible to see a perfectly symmetrical waveform. There are a couple factors that contribute to this.
First, while some instruments will just pull the air back and forth by roughly the same amount, some instruments will be accompanied by a positive pressure while being played (think voice, or brass, or woodwinds). So while there will be variations in the pressure, there might ultimately be an overall positive pressure.
Secondly, and more importantly, is a mathematical effect called interference. Whenever you hear a sound, you are usually hearing more than one frequency at a time. For harmonic sounds like musical instruments, this will mostly be limited to harmonic overtones. For unpitched sounds like drums, or complex sounds like speech, there will be a complicated array of a possibly infinite number of frequencies. These waves have varying frequencies and amplitudes, and interact with each other in complex, hard to predict ways. Where two waves happen to have a coincident peak (or trough) -- called being "in phase", they will add together to make that peak stand out more. OTOH, if two waves are "out of phase" (one's peak aligns with the other's trough) they cancel each other out. Depending on which peaks and troughs are aligned, this can make the waveform appear taller on one side or the other.
However, I believe that if you were to zoom in, and add all the area between each peak and the centerline, and subtract all the area between each trough and the centerline, the net result would be about zero (or perhaps a small positive value due to the first reason listed above).
As a side note, there's also a fair amount of graphical aliasing going on, from squeezing more peaks and troughs into a region then there are pixels to represent them. This is why I say that you'd have to zoom in on the original soundwave (just zooming in on the picture won't work, because that level of detail is already gone).
