The next instant, he saw Elena’s gaze again, felt it sear his memory. He halted. A sudden idea threw back the chill. It sprang practically full-grown into view as if it had been maturing for days in the darkness of his mind, waiting until he was ready.
Covenant conceives of the idea of sacrificing his daughter rather than himself. All he had to do is manoeuvre her into taking full responsibility in fighting Lord Foul, and he can (Phew) stay in the calm shadows of total irresponsibility.
Here is the exact nature of Covenant's real dilemma. To believe in the Land and take responsibility for saving it or 'unbelieve' in the Land and avoid all responsibility for saving it.