How would you go about getting the small signal transfer function for this inverting circuit?
One way to get a reasonably interesting, but not impossible to calculate, answer is to assume the amplifier has a one-pole frequency response, and an arbitrary real output impedance.

Keeping the output impedance \$R_A\$ as a free parameter, you should be able to qualitatively predict the overall behavior with the given load, and also say something about how the step response would depend on the amplifier's output rise-time and the resonant frequency of the LC load.