Why should this surprise anyone?
Prostitution is the world’s oldest profession. Prostitutes used lipstick to let johns know they were hookers.
Or is the color red supposed to be the surprise?
Since natural ingredients were all the women had to make cosmetics out of at that time, you might want to look at the predominance of deep red/red in the minerals, clay, etc those cosmetics were made of. Just like the stuff they ground up to make eyeshadow was predominantly green or blue, and eyeliner ingredients-kohl/charcoal were black.
Since we know that human females of all social groups have been adorning themselves with colored paint/makeup, jewelry, etc from well into pre-history, it makes a lot more sense to look at the source of the cosmetics than to “tar” the wearer of red lip color as a prostitute-plenty of women today like red lipstick who are not hookers-mostly brunettes, because it looks good with their dark hair. As a redhead, I do not wear red lipstick, and neither do any blondes I know-but entertainers of all shades wear it on stage, because it can be seen even by the audience in the cheap seats, just like bright blue eyeshadow and glitter-infused body paint, etc...
Red being a preferred color for hookers was certainly written about-but it was a lot later than 3600 years, as was their wearing of red dresses, putting up red lights, etc. Based on what you are saying, have all men who have tattoos always been bad boys or cruel and ruthless warriors in the human family? I do have a lot of friends and neighbors who are veterans who have tats-they are not outlaw bikers or serial killers, either. I think your assumption is a bit too broad...