This is a Buddhist proverb and my informant doesn’t remember where he heard it. It means all lust leads to sorrow. My informant likes it because it reminds us that our spiritual well-being is often more important to our happiness than our physical world; he takes lust to mean want in general rather than only sexual want. Buddhism says that attachment is what leads to suffering, so detaching oneself from desires in the physical world will lead one away from suffering.
Humans are often said to feel a sadness after an orgasm, perhaps because it is a let down; the ecstasy is just suddenly gone. The French call it le petite mort, meaning little death. In this way, lust does directly lead to grief. On a larger scale, though, all sexual and romantic attachment usually leads to grief due to human drama and the breaking apart of relationships. And on a scale larger than that, all human wants, which the word lust could be used to represent, lead to grief because having our desires in the physical world fulfilled doesn’t bring us lasting happiness. We get what we want and then that’s it; there will be a void again afterwards. Beyond that, everything is ephemeral, so it may not even be important that we got what we wanted, be it reaching a goal or acquiring a physical object. Buddhism recognizes this and communicates it via this concise proverb.