Concerning the change in wavelength (and hence change in lattice constant) due to the refractive index of the gas, this effect is tiny. We consider it in section 6, on p17 and show that the correction to the refractive index is of order 10^-9 for our parameters. This is to be distinguished from the effective change in the cavity length which, due to the resonance effect, is substantial and is precisely what lies behind the amplitude modulation of the lattice.
The estimated accuracy is $10^6$ that does not sound great.