I think it's a learned /expression/ of reproductive signalling.
I think of lipstick as just a human equivalent of a monkey with a big red butt (which is natural, but doesn't serve any purpose other than to let other monkeys know they're in heat).
They're human ways of drawing attention to sexuality. In our society we can't paint our genitals, so we paint another set of lips. Or our fingernails, etc.
When a child picks lipstick, however, they're not being sexual, just emulating adults. They same way they copy adults tone (ever heard a kid 'scold' another kid, the same way their parents would?) Most infant animals do that too.