You can activate Liliana’s first ability even if some or all players will be unable to discard a card.

When Liliana’s first ability resolves, first the player whose turn it is chooses a card in hand without revealing it, then each other player in turn order does the same. Then all the chosen cards are discarded at the same time.

When Liliana’s third ability resolves, you put each permanent the player controls into one of the two piles. For example, you could put a creature into one pile and an Aura enchanting that creature into the other pile.

A pile can be empty. If the player chooses an empty pile, no permanents will be sacrificed.