LORELAI: The money goes to charity. I look cute. Case closed. Oh finally, the coffee cavalry arrives.
Lorelai is referring to the classic trope in Western films where the US Cavalry charges over the hill just in time to save the battling settlers from Indians. It was a favourite in D.W. Griffith films from the early twentieth century.
Lorelai is saying the coffee is arriving just in time to rescue her from the conversation. Apparently when she is wearing a cowboy hat, she thinks in Western cliches.