I skimmed through Streetcar and couldn't find anything about which cigarettes Stanley and Stella liked to smoke. I also couldn't find anything about Stanley disliking Lucky Strike cigarettes.
I did find, in Scene 3, that Mitch offers Blanche a "Luckies" (Lucky Strike) cigarette, to which Blanche responds, "Oh, good." Perhaps the Lucky Strike brandname is used as a symbol for Blanche's attitude toward life. She is a dreamer, a romantic, a person who believes in luck and magic. In Scene 9 she tells Mitch, "I don't want realism. I want magic!"
Interestingly, Blance mentions three authors whose works she has taught in her high-school classes: Nathaniel Hawthorne, Walt Whitman, and Edgar Allan Poe. Hawthorne often deals with mystical themes, such as witchcraft; Whitman's poems were considered to be obscene in his time; Poe often wrote of horrible tragedy and catastrophe. These three themes -- magic, sensuality, and tragedy -- are major elements in Blanche's life.
Stanley, in contrast to Blanche, does not really believe in luck. When Pablo, one of his card-playing cronies, wishes him bad luck, Stanley replies:
You know what luck is? Luck is believing you're lucky...To hold front position in this rat-race you've got to believe you are lucky.
According to Stanley, "luck" is not some mystical force that resides outside of a person. Rather, luck is self-confidence. If you believe in yourself and do what is necessary to win, you will win.
If you can find the passage in which Stanley expresses his dislike for Lucky Strikes cigarettes, you can explain it as above.