Can you specify what you are talking about?
If you are talking about the CG of the object to be lifted and say it was a object of some type, (e.g. fractionator, oxidizer, reactor, storage tank, generator etc...) then the lifting CG would be one where the internals, ladder, platforms, liquids etc... are not on or in the unit. The operating CG is when the unit is in operation and all the additiional weights are in place.