Is there an Ian in the book that this woman could be said to be "serving"? Perhaps the author isn't being literal but is making a reference to the character Leana's relationship with the character Ian.
Actually this could make some sort of sense if Leana is actually a shortened form of her full name. Many Gaelic surnames starting with Gill- go back to forms that meant "servant of" some saint or religious figure. Gilchrist was "servant of Christ" and Gilfillan "servant of St. Faolan", for example. I have sometimes seen Gillian (with a hard "g" sound) explained as a Scottish male name meaning "servant of St. John". So perhaps the author is implying that the character Leana's full name is something like Gilleana or Gilliana.