Analysis on the output waveform from LTspice
Opamps are also limited in the maximum slew rate they can drive. Looking at the LT6202 datasheet, the slew rate spec is typically 24V/us. That looks to be about the rate you are driving it in the simulation.

Try reducing the amplitude of the input signal. You should find that the distortion is reduced. The frequency is the same, but the maximum rate of change of voltage is smaller.