This is the EIS measurement I did on the Li-ion battery and sometimes I see this kind of Lissajous figure? I measured this directly in a assembled cell, meaning I have everything there, anode, separator, electrolyte, and cathode.
I guess that you vary the potential slightly around a potential offset from OCV and monitor the current (?) - at what frequency?
What you see is that the current fluctuates, meaning that the basic requirement for doing EIS (equilibrium or at least steady-state) is not fulfilled. This is because the system you are testing is changing with time (corrosion, break-down of passivation layers, disintegration of electrode particles etc etc). Before doing EIS you have to wait until the current fluctuations are smaller than the currents resulting from the potential perturbations you impose (if in potentiostatic mode).