Why are there multiple side lobes in the glide slope signal from an ILS?
All directional antennas have sidelobes (and all real antennas are at least somewhat directional). I won't get into detail of the fundamental physics reasons behind that, as that's beyond the scope of the aviation stack exchange, but briefly it's related to diffraction and the Fourier relationship between the aperture distribution and the far-field radiation pattern.
Various design techniques can reduce the amplitude of the sidelobes, sometimes to the point where they're undetectable or at least insignificant. However, these all involve tradeoffs that compromise other performance parameters, size or cost, so if the sidelobes aren't problematic or can be easily avoided operationally, it's not worth trying to suppress them. Also, most glideslope antennas use passive phased-array techniques, and phased arrays are especially prone to sidelobe generation (called grating lobes in that case).
The ILS transmitting antennas looks to be an array of yagi antennas. Those antennas should have a tight beamwidth, but the penalty for being able to "squirt" energy in a single direction is that you have multiple sidelobes coming off the side and back side of the antenna. The more antenna elements you add to a single antenna, the more lobes you'll get.
Look at figure 2.1, then compare figure 3.2 and 3.3 at http://www.researchinventy.com/papers/v2i12/E0212026035.pdf
You'll probably get a more in depth answer from the amateur radio guys who are more experienced that I am.