Crane's father was Winthrop Murray Crane, an American millionaire and former governor of Massachusetts. Her mother was Museum of Modern Art (MoMA) co-founder Josephine Porter Boardman. Louise smoothly moved into the role of patron of the arts. She was a prominent supporter of jazz and orchestral music, initiating a series of "coffee concerts" at MoMA and commissioning a vocal and orchestral work by Lukas Foss. She represented musicians, including Mary Lou Williams. Crane collaborated also with her mother in sponsoring musical works.
Crane met Elizabeth Bishop while classmates together at Vassar in 1930. The pair traveled extensively in Europe and bought a house together in 1937 in Key West, Florida. While Bishop lived in Key West, Crane occasionally returned to New York. Crane developed a passionate interest in Billie Holiday in 1941.
Crane published ''Ibérica'', a Spanish-language review, with her partner, Victoria Kent, from 1954 to 1974. ''Ibérica'' featured news for the expatriate Spanish community in the United States. Kent was a prominent member of the Spanish Republican party, opposed to Franco. Many prominent writers, including Salvador Madariaga, contributed to ''Ibérica''.
Crane lived for years in an 18-room apartment on the fourth floor of the 820 Fifth Avenue building, a luxury cooperative in Manhattan, New York City. Located at the northeast corner of East 63rd Street on the Upper East Side, the 12 story limestone-clad was designed in the neo-Italian Renaissance palazzo style by Starrett & van Vleck, and was built by Fred T. Ley in 1916. The fourth floor is one of only a few units in the building which have changed hands multiple times in the last 10 or 20 years. After Crane’s death in 1997, the apartment was sold to Tommy Hilfiger for around $10,000,000.