"Lean" is mostly one of those nostalgia/status things. Unlike the aforementioned rich old white guy Rush Limbaugh, financially destitute young black guys (as rappers tend to be before they make it big) basically had access to two types of opioid: Codeine-based cough syrup and heroin. Promethazine doesn't really "improve" the high beyond potentiating the sedating effects of the codeine; it's just an old phenothiazine-type antihistamine, so it blocks a whole bunch of histaminergic, serotonergic, dopaminergic, adrenergic and cholinergic receptors.
When Southern Hip Hop blew up on the scene, doing "lean" became a point of nostalgia, of pride, and of belonging... a way of showing that you remembered being a kid on the street. And even hip-hop fans who had grown up comfortably middle class started using lean to imitate their idols.
Naturally, this caused regulations around promethazine/codeine to be tightened, and some products to be withdrawn from the market (like Actavis, formerly considered the number one brand of codeine/promethazine syrup), which only made it more desirable for young rich guys with way more money than common sense (as rappers tend to be after they make it big): A product that simultaneously gave you street cred as an ex-poor-person, AND let you brag about how much money you were willing to wastefully spend as a member of the nouveau-riche.
These kinds of changes happen all the time: Until the late 19th century, lobster used to be considered a near-worthless byproduct of commercial fishing, a gross water bug barely considered appropriate for even indentured servants and prison inmates to eat on a regular basis. Once people figured out how to keep lobsters alive and refrigerated for transport, however, the rich people of the New York upper class suddenly made it a highly desirable delicacy; presumably, the associations around the product and its origins also changed around that time: Where originally people would associate lobsters with the abject poverty of Maine fishing villages, the upper crust living in the polluted city of New York would over time come to associate the coast of New England with clean air, and fishermen as a romanticized picture of physical strength and virility.