My very basic voltage-controlled amplifier gives an asymmetric waveform?
The basic reason for the distortion is that the FET's Drain-Source resistance varies with voltage. In this graph of output characteristics for the LSJ689 you can see that even in the 'linear' region the relationship between Drain current and voltage gets less linear as amplitude increases. It also get worse as the Gate is biased further toward cutoff. Unfortunately this causes even more distortion at lower gain settings, when input amplitude may be higher.         



You are making it worse again because you have the Source and Drain swapped around, so the feedback signal is modulating the Gate-Source voltage.

Dividing Drain-Source voltage by Drain current in your LTspice simulation, we get this:-



Drain-Source resistance varies from ~306&ohm; to 330&ohm; (8%) as the signal voltage goes from peak positive to negative. The varying resistance alters the gain causing positive peaks to be amplified more.  

With Source and Drain the correct way around the resistance varies from ~310&ohm; to 326&ohm; - about 1/3rd less - but the distortion is still significant. 

This effect can be reduced by attenuating the input signal and increasing the gain to compensate. With the FET wired with Source to Ground, input reduced to 50mV and R1 increased to 4k the resistance variation is only 1%.