Recall that Jude said he could power Abyss and HE-6, in a pinch.
How much volume are you looking to use? How much do you use currently with your LCD-3?
I have been quite pleased by how well it drives HE1K. And I have heard HE1K (mine) and LCD-4 (at a recent meet) powered by the same amplifier, at basically the same volume. No - it was not the Prime. But I do not expect any trouble if you plan to use the Prime with LCD-4.