Here's my nonexpert opinion.
I've never owned an induction cooktop, but a cursory search of the Internet led me to a site where someone suggested that the switching frequency for induction cooktops usually varies between 24-48kHz. This switching range should be outside of the audible range of humans and you should not hear anything from the switching power supply (humans can hear up to 20kHz).
In this case, however, you also have some low voltage lights? Do these low voltage lights have a switched mode power supply to convert the line current from AC to DC? Or do they use a step-down transformer and rectifier? (I'm guessing they use a SMPS as they are probably <100W?)
I'm assuming your induction cooktop requires a 240V circuit?
Here are a couple of theories:
1) A beat frequency in the audible range between the switching supplies, which may switch at slightly different frequencies. You can't hear each one independently, but perhaps when they are both on at the same time you hear a hum at the difference in their switching frequencies (my apologies to all previous physics teachers if I am misinterpreting this concept here!).
2) My other idea (slightly more complicated) is that perhaps your lights - more precisely the SMPS - is causing a voltage harmonic on one of your phases. Hold that idea, and let's look at the cooktop. I imagine that in the cooktop (again, stress that I've never pulled one of these things apart, so I'm guessing as to how they operate) uses some sort of AC-DC-AC conversion process to create the high frequency waveform that ultimately does your cooking. If this is the case, both phases are likely rectified as they come into the unit (using something like this full-wave rectifier -
http://www.falstad.com/circuit/e-fullrect.html) and combined to create a relatively ripple-free DC waveform that can be chopped to the necessary high frequency.
Now, if one of your phases has a voltage harmonic, this harmonic could be passed through the rectifier (assuming no or filters not tuned to this frequency) and increase the ripple in your output waveform in the induction cooker, perhaps resulting in an audible hum.
Hmmm...that's the best I've got.
So if you do have a SMPS on your low voltage lights, I think the easiest thing to do would be to switch it out with a step-down transformer setup to see if this helps.
Here's a little reference I just pulled up on harmonics caused by SMPSs that seems useful:
http://www.copperinfo.co.uk/power-quality/downloads/pqug/31-causes-and-effects.pdf