In lassi, the yogurt is the "hero" of the drink.
In smoothies, the fruit is the "hero" of the drink.
Hero being the star, or main focus, of the dish/drink.
It's all about the ratio.
Lassi doesn't require fruit, but one may incorporate it if one chooses. But it's mainly a yogurt drink.
Smoothies don't have to include yogurt, but one may incorporate it if one chooses. But it's mainly a fruit drink.
Lassi (pronounced "lussy") is made from yogurt. It may also contain fruit, often mango, but it doesn't need to. At any rate the main ingredient is always yogurt. A smoothie contains mostly fruit, although it could also contain yogurt, but most don't.