I Is the mass defect still considered with invariant mass?

[PeterDonis]

You could also use solar energy to grow the food needed for a human to lift the book.

Yes, but that is just admitting that in fact the Earth (or the Earth plus the book plus the human) is not a closed system. There is energy flow across its boundary in both directions. What's more, if you are taking this energy flow into account, the system is not stationary either, so the notion of "potential energy" is not even well-defined. Obviously this is no longer "as simple as lifting a book", nor is it any good as an illustration of any point about potential energy or invariant mass.

So either you bring in complications that make the whole subject of this discussion pointless, or you accept a simple model in which the Earth-book system is closed, at least on the time scale required to lift the book (note that this time scale is much shorter than the time scale required to capture solar energy and grow the human's food), and in that model, the externally measured mass does not change when you lift the book.