As Liliana's Triumph resolves, the opponent whose turn it is (or, if it's your turn, the next opponent in turn order) chooses a creature to sacrifice, then each other opponent in turn order does the same, knowing the choices made before them. Then all the chosen creatures are sacrificed at the same time. Then, if you control a Liliana planeswalker, in the same order, each opponent chooses a card in their hand without revealing it, and those cards are discarded at the same time.

You can cast Liliana's Triumph even if some or all of your opponents will be unable to sacrifice a creature. If you control a Liliana planeswalker, they'll still discard a card, even if they couldn't sacrifice a creature.

Whether you control an appropriate planeswalker is checked only as the spell resolves.

Controlling more than one planeswalker of the appropriate type won't have any more of a benefit than just controlling one.