Equally viable is the hypothesis that the "avatar" is an injection of the Prince entering past the Lunar Lattice by force or by a back door. Think of it as sort of like http://en.wikipedia.org/wiki/Quantum_entanglement, in the sense that the Prince can be in two places at the same time. Or, maybe it is morel like shoving a Play-dough blob through a small opening: most of it stays outside of the Lunar Lattice, but some comes through. It is part of the whole, and is connected in ways not visible to the naked eye (maybe another dimension, or through wormholing).
At least, that's how I think of it. Because a separate entity - the whole "avatar" thing - just seems kind of boring and very cliche and not very rational.