If there are no instant or sorcery cards in your graveyard as Living Lore enters the battlefield, it will enter the battlefield as a 0/0 creature and be put into its owner's graveyard due to having 0 toughness.

If an instant or sorcery spell puts Living Lore onto the battlefield, that spell is still on the stack while you choose a card to exile. You can't exile it with Living Lore.

If Living Lore leaves the battlefield, the ability that defines its power and toughness will lose track of the exiled card. Its power and toughness are 0 in other zones.

Similarly, if the exiled card somehow leaves exile while Living Lore is on the battlefield, it will become a 0/0 creature.

Living Lore's last ability will trigger whenever it deals combat damage, no matter if that damage is dealt to an opponent, an opposing planeswalker, or a creature it's blocking or being blocked by. You choose whether to sacrifice Living Lore as that ability resolves. If Living Lore has already left the battlefield, perhaps because it was dealt lethal damage at the same time it dealt damage, you can't sacrifice it.

You may cast a sorcery this way even if it's not your turn.

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, such as that of Tormenting Voice, those must be paid to cast the card.

If a spell has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.