Lydgate turned his dark eyes on her and watched her as she delicately handled the tea-service with her taper fingers, and looked at the objects immediately before her with no curve in her face disturbed, and yet with an ineffable protest in her air against all people with unpleasant manners.
There are no more uses of "ineffable" in the book.
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They were mystical experiences and were ineffable (incapable of being described in words).
She had been housed with the captain while the rest of them had gone on to entertain the commander; the doctor had reserved her, implying to the commander that she was not a virgin like the others, who would offer him the salubrious and then other ineffable effects of his taking their maidenhood, which to a soldier is like an amulet of life and rebirth.