Non linear behaviour of a pure LC: Is it real or LT Spice is broken?
Where does this mathematically come from?

Starting a sinewave from any point in its waveform is creating a transient. Prior to the sinewave being present there was 0 volts then suddenly you start-up a sinewave. This creates a transient response in the LC filter and, because it is highly resonant (limited only by any parasitic elements LTSpice defaults to), you get a resonant response that theoretically should take infinite time to decay. The high-frequency superimposed on the sinewave is the resonant frequency. Just look at the spectral result - it's at 50 kHz.
If you applied a step input in the s-domain you would get the same sort of transient behaviour.