A spell cast using flashback will always be exiled afterward, whether it resolves, is countered, or leaves the stack in some other way.

If a split card gains flashback, you pay only the cost of the half you're casting.

You can cast a spell using flashback even if it was somehow put into your graveyard without having been cast.

"Flashback [cost]" means "You may cast this card from your graveyard if the resulting spell is an instant or sorcery spell by paying [cost] rather than paying its mana cost" and "If the flashback cost was paid, exile this card instead of putting it anywhere else any time it would leave the stack."

To determine the total cost of a spell, start with the mana cost or alternative cost (such as a flashback cost) you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell is determined only by its mana cost, no matter what the total cost to cast the spell was.

If a card with no mana cost gains flashback, it has no flashback cost. It can't be cast this way.

If you cast an instant or sorcery with in its mana cost this way, you still choose the value of X as part of casting the spell and pay that cost.

If you cast a spell with flashback, you can't pay any alternative costs such as overload costs. You can pay additional costs such as kicker costs. If the spell has any mandatory additional costs, you must pay those to cast the spell with flashback.

If a card has multiple instances of flashback, you may choose any of its flashback costs to pay.

You must still follow any timing restrictions and permissions, including those based on the card's type. For instance, you can cast a sorcery using flashback only when you could normally cast a sorcery.

If a card with flashback is put into your graveyard during your turn, you can cast it if it's legal to do so before any other player can take any actions.

Lier's last ability allows you to cast adventurer cards in your graveyard as Adventures and omen cards in your graveyard as Omens using the flashback it grants. This is because the alternative characteristics of those cards are considered when determining whether or not those spells can legally be cast. Note that only the Adventure or Omen can be cast this way. For example, if you control Lier and you have Bonecrusher Giant in your graveyard, you can cast Stomp with flashback, but not Bonecrusher Giant.