A libation is a drink poured out as an offering to a deity. It was a popular practice in Ancient Greece where people regularly poured libations to the gods as part of religious rituals.
In "Editha," George says that he got drunk after pouring too many "libations" of whiskey down his throat. He tells Editha that he was consecrating himself to her god of battles. This indicates that George is still not enthusiastic about the prospect of going to war and is only really doing it to please Editha. It is her god to which he offered libations, not his. Even so, Editha's not best pleased. She makes George promise that he won't touch a drop of the hard stuff ever again. She wants him to remain healthy and strong for his country. As always, she's thinking about the war, which she stubbornly insists on romanticizing.