I wonder if at some point there wasn't a conflation of Red Cross and Red Sun.
There's some documentary evidence that the brands produced by the W.R. Irby Branch of the American Tobacco Company in New Orleans (of which Red Sun was one) were chiefly distributed in Louisiana, Texas, and surrounding areas. Prior to selling out to the ATC in 1899, Irby was primarily a producer of cigars, cigarettes and snuff and that product line stayed pretty much the same afterward.
P. Lorillard had a huge factory in Jersey City, and had no factory in Louisiana. But products were shipped by rail all over the place of course. Here's an ad for a Salt Lake City grocer from 1888, and he's offering Lorilliard's Red Cross tobacco for sale.
