Inverting a Sine Signal
The OP-07 is a great little device but not suitable for your application. The signal coming from the 555 and LC filter is about 10 kHz and has an amplitude of about 14 volts peak-to-peak and the slow OP-07 just cannot keep up. It's output is slew rate limited to typically 0.3 volts per μs: -

And that means a 14 volt change in output amplitude will take nearly 47 μs and might be as long as 140 μs. Bear in mind that 10 kHz has a period of 100 μs. So, what you get is a rather triangular shaped output waveform (as you can see if you look closely): -


What circuit should I build to successfully invert this sinusoid
signal?

A much quicker op-amp is the likely answer. Or, if you can live with a smaller amplitude sinewave, reduce the amplitude.