LUKE: I’m an island.
LORELAI: Luke, I’m sorry about all this, but I’m not anticipating the inn catching fire ever again, so it’s a one time only thing, okay?
Luke refers to the famous quote, “No man is an island” from the poem “Meditation VII” by John Donne. He may also be thinking of the 1965 Simon & Garfunkel song, “I Am a Rock”, which says, “I am a rock, I am an island”, written from the point of view of someone isolated and emotionally detached.
Of course, for all his reclusive ways, Luke is never an island, he is always there for his community. And of course Lorelai always wants him to do “just this one thing” for her, repeatedly. He never says no.