I already answered 4 times !!! See my previous answers for similar questions (first, very old was about Li (I can't find), next one also (#1), two other - about Na (#2 and #3). In fact, situation for Li and Na is very similar).
Very intresting discussion... The student asked and disappeared ... Maybe after the holidays, if he is still interested in this question, he will return to the problem. Depends on many circumstances. But the answers are ready!
Is there will be an issue in the mpedance Spectra, if I am unable to scratch out completely the lithium oxide layer from the lithium foil ( foil thickness 0.3 mm ). Will it introduce another interference in the Spectra since I am getting only two semi circle ( cell configuration Li/saple/Li)
The 0.3 mm foil it is not thin imho. Thin foil is 0.05 mm or less... 0.3 mm foil it is quite possible to clean on rough polyethylene - read the links to my old answers.
Of course, if it is not oxidized through. Then you have to think about the atmosphere in the glove-box as well as about storage conditions.
2) The Z-values, in your Nyquist, plot are, at least, 4-orders higher than expected for a liquid Li-electrolyte. If your Li-electrolyte (CPE) is a solid one, then start using a liquid Li-electrolyte (Z-values near 1 Ohm) by fixing, firstly, the surface issues of (the corroded surface of) the Li electrode(s).
1) You can try to drop(-wet) a small drop of liquid[1] Li-electrolyte (-wetting) on each one of the Li electrode(s') side, e.g. Li//CPE and CPE//Li interfaces, and re-measure (both) Z-spectra.
2) Also, you can use a higher VDC polarization voltage[2] value, say a value of: 100 to 500mV for 1 hr.
1. It will reduce a lot the (serial) Z of the Li electrodes (interfaces), in order to focus better on your main target, the solid Li-electrolyte, it's Li-conductivity.