My short answer would be that it is virtually impossible but depends on how good results you expect.
The solution your intuition draws you to, and which would work in certain cases, is phase cancellation. Basically, if you have two sound sources, exactly the same, and reverse the polarity of one they will cancel each other out.
The simplest example of this would be a DC source at, say 5 volts sent to a speaker cone. This would push the cone outward. If you add to this another DC at -5V the sum will of course be zero and the cone will go back to its original position.
With a complex waveform the same thing will happen.
The key here is "exactly the same". Any difference in volume, frequency response and phase will make more or less or all sound come through.
This approach would be possible with at least useful result if the speaker's microphone was in a fixed position and the soundtrack was played back all the way through with the speaker in position but silent. Ideally all factors should be as close as possible to the actual lecture. You could then exactly match the two takes in time and possibly, if done correctly, at lower the volume of the soundtrack (but gain 6db more noise).
In your case this wouldn't be possible. The original sound will differ too much from the sound recorded by the microphone from the speakers, each step introducing differences in frequency response and phase.
I think in your case you will have to yet and use EQ to as far as possible isolate the speech. The results would be far from perfect, especially since the frequencies prominent in speech is usually also prominent in music, but might be better than nothing.
Some linear phase EQ:s are able to show the spectrum and make changes over time. This means a lot of careful manual work but might be worth it in the end. Aggressive editing in this regard will create artifacts in the remaining sound so there's always a trade-off.
There are of course programs, usually rather expensive, that deals specifically with removing unwanted sound from recordings and these technologies are getting more and more advanced. It was ten years ago I last used such utilities but back then Izotope had some impressive solutions to deal with noise. You might have some luck there. This seems to be their on latest tool set :
Good luck! Although this might not be the answer you were hoping for I hope you find a working approach.