“Green Dolphin Street” is a 1947 historical drama film released by Metro-Goldwyn-Mayer and based on the novel by Elizabeth Goudge.
In the 1840s, on an island in the English Channel, two sisters, Marguerite (Donna Reed) and Marianne Patourel (Lana Turner), daughters of the wealthy Octavius Patourel (Edmund Gwenn), fall in love with the same man, William Ozanne (Richard Hart).
Having settled in New Zealand, William writes a letter to the family proposing marriage to one of the sisters.
The father cannot read the letter, so the mother does.
The letter asks for Marianne’s hand in marriage.
Marianne, decides to set off for New Zealand to be with him.
William expecting Marguerite, realizes later when he sees Marianne come off the boat that he wrote the wrong name in the letter.
When the mother is on her deathbed, she tells Marguerite a story about love and marriage and tells her to apply it to her own life, as a hint that William was not the man for her.

Lana Turner plays Marianne Patourel.

MGM tought that Lana was ready for more heavy dramatic projects after her work in “The Postman Always Rings twice“, they casted her as the spirited heroine, Marianne Patourel. Lana was in costume again for the first time in 6 years and her characterization required her to become a brunette as well. The film was a huge hit with the public. 
In PM, Cecilia Ager wrote: “No matter what the century Miss Turner’s consigned to, she brings to it her own firm-fleshed, contemporary glamour. Wherever she is, she stands out as Lana Turner, unquestionable, one of Metro’s most glittering productions all by herself. In a movie dedicated to production values, Miss Turner right or wrong is most eminently right.”
Lana herself was very proud and fond of her role in this film. A contributing factor to Lana’s special fondness for this film is that it was made in the height of her romance with Tyrone Power.

The song “On Green Dolphin Street” (originally entitled “Green Dolphin Street”) was composed by Bronisław Kaper with lyrics by Ned Washington. Here is the original version:

The title song of this epic costume drama inspired one of the great jazz recordings of the ’60s and ’70s. The first to make the jazzified “Green Dolphin Street” famous was probably the version by Miles Davis. Lana had a 78 record of it which she played often.

Trailer:

You can watch the film here.

Lana Turner did a lot of movies. She really loved being a moviestar.
Here are the most important films in which she starred. Just click the links for more info, photos and videos.

20 April 1937: A Star Is Born
9 Oct. 1937: They Won’t Forget
24 Oct. 1937: The Great Garrick
1 Jan. 1938: The Adventures of Marco Polo
22 July 1938: Love Finds Andy Hardy
12 Aug. 1938: Rich Man, Poor Girl
9 Dec. 1938: Dramatic School
28 April 1939: Calling Dr. Kildare
18 Aug. 1939: These Glamour Girls
29 Sept. 1939: Dancing Co-Ed
19 April 1940: Two Girls on Broadway
19 July 1940: We Who Are Young
25 April 1941: Ziegfeld Girl
12 Aug. 1941: Dr. Jekyll and Mr. Hyde
2 Oct. 1941: Honky Tonk
18 Febr. 1942: Johnny Eager
27 Aug. 1942: Somewhere I’ll Find You
1 April 1943: Slightly Dangerous
19 Aug. 1943: Du Barry Was A Lady
13 Nov. 1943: The Youngest Profession
23 Aug. 1944: Marriage Is a Private Affair
8 March 1945: Keep Your Powder Dry
1 Oct. 1945: Week-End At The Waldorf
2 May 1946: The Postman Always Rings Twice
5 Nov. 1947 : Green Dolphin Street
1 Nov. 1947: Cass Timberlane
29 April 1948: Homecoming
20 Oct. 1948: The Three Musketeers
1 Sept. 1950: A Life Of Her Own
2 March 1951: Mr. Imperium
5 Sept. 1952: The Merry Widow
25 Dec. 1952: The Bad And The Beautiful
25 Aug. 1953: Latin Lovers
1 May 1954: Flame And The Flesh
7 Sept. 1954: Betrayed
13 May 1955: The Prodigal
4 June 1955: Sea Chase
14 Dec. 1955: The Rains Of Ranchipur
12 Jan. 1956: Diane
13 Dec. 1957: Peyton Place
30 Jan. 1958: The Lady Takes A Flyer
2 May 1958: Another Time, Another Place
30 April 1959: Imitation Of Life
23 June 1960: Portrait In Black
19 July 1961: By Love Possessed
2 Nov. 1961: Bachelor In Paradise
25 Dec. 1962: Who’s Got The Action?
24 Febr. 1965: Love Has Many Faces
27 April 1966: Madame X
30 April 1969: The Big Cube
7 Nov. 1974: Persecution
27 Oct. 1976: Bittersweet Love
31 Oct. 1980: Witches Brew
21 May 1982: Dead Men Don’t Wear Plaid

Sources: Wikipedia, IMDB, Rotten Tomatoes, Lana’s biography “Lana, the Lady, The Legend, The Truth“, “The Films Of Lana Turner” by Lou Valentino and “Lana Turner, The Memories, The Myths and The Movies” by Cheryl Crane.