LORELAI: I’m a nomad … I am the lonely wanderer.
A nomad is someone without a settled home who regularly moves from place to place. Examples of nomads include hunter-gatherers, pastoral herders, tinkers, traders, and itinerants.
Lorelai is possibly referring to the 1963 country song by Slim Whitman, “(I’m a) Lonely Wanderer”. I’m mostly basing this on the fact that she immediately references another country singer.