Lily's Ocean was a geographical feature on the planet Alpha Centauri B II and was named by Zefram Cochrane who thoroughly enjoyed naming the many locations on the world after exploring it. The thirty buildings that comprised the Cochrane Institute of Alpha Centauri sat on a hilltop that oversaw Lily's Ocean to the east. (TOS novel: Captain's Glory)

Presumably, its named after his colleague Lily Sloane.