This is quite a heay one. I don't see how you could possibly apply a method like in the paper for a non-periodic surrounding (which I assume your electrode to be while Li is moving). In principle you can get vdW-parameters by performing high end wavefunction calculations such as higher order coupled cluster but I think that will be too computationally demanding for your situation.

Of course you can try DFT using a vdW-correction like Grimme or Tkachenko/Scheffler, but don't be surprised if you observe overbinding to some extent.

dear @Jurgen , what is the exactly problem in applying this described method to calculate the potential between moving Li ion and metal cation in the periodic cathode structure(orthorhombic in our case), if we want to describe very specifically activation barrier of Li hopping.