Fatima cigarettes featured a blend of Turkish tobaccos but were produced in the United States. They were phase out of production by about 1980.
Chesterfield is a brand of American cigarettes named for Chesterfied County, Virginia, and popular in the early 20th century. They are still being made.
Camel is a brand of American cigarettes containing a blend of Turkish and Virginia tobacco.
Lucky Strike is a brand of American cigarettes featuring tobacco that's toasted rather than sun-dried.
All these brands carry a certain amount of cachet, but they're evidently not good enough for Elliott, who prefers Egyptian cigarettes. However, by 1919, Egyptian cigarettes were falling out of fashion.