I do not understand if it's Tibetan Buddhism saying lower, middle, or greater yanas, or only Tibetan Buddhism only.
Reference to the Chinese Sutras I studied, it would be Śrāvaka, Bodhisattva and Buddha yanas. Or sometimes five yanas: Śrāvaka, Arhat, Pratyekabuddha, Bodhisattva and Buddha. These yanas are depending on the nature/inclination of the students that they naturally choosing their vehicles. In general, Sravaka, Arhat and Pratyekabuddha responding to life as an abode to be escaped from, their main concern is a jailbreak, or liberation. But the Bodhisattva and Buddha are liberation and enjoyment, or total mastery. All yanas have happy ending, just that they have different taste buds, like some people like beer, some wine, some whisky... :)
So this is not the Buddha be partial or judgemental, just providing all different drinks for all different drinkers that pleased the most their taste buds. It wouldn't be a good bar if only offering one type of drink, huh?