LC transient response to DC is identical to the LR circuit.

Its LR and RC, not LC.

Yeah the waveforms are similar, but current and voltage are inverted in the components. Capacitor lags voltage peaks current, inductor lags current peaks voltage.

YOu have an LR circuit, your cell voltage has the same waveform of a resistor voltage in series with an inductor.

You have exactly the blue curve in your first pic, the inductor current waveform, multiplied by the resistance of your resistor (water capacitor), gives you the "water capacitor" waveform.