This is the song which plays while Luke sadly watches Lorelai and Max together on their date in the snow.
Someone to Watch Over Me was written by George and Ira Gershwin, for the 1926 stage musical Oh, Kay!, where it was sung by Gertrude Lawrence. It went on to become a jazz standard, recorded numerous times, and several times used in films – including What’s Up Doc? (1972), referred to earlier.
The version used on the show is sung by Rickie Lee Jones, from her 2000 album It’s Like This.