You must choose at least one mode if you can. If there are no legal targets available for the first two modes, you must choose the last mode. Notably, the last mode can target any player, even one who has no cards in their graveyard. In the unusual case there are no appropriate cards in exile to target and no player may legally be chosen as a target, the ability is removed from the stack with no effect.

The first and second modes of Sentinel of Lost Lore's ability can target any face-up exiled card that has an Adventure as long as it's owned by an appropriate player. It doesn't matter whether the card was cast as an Adventure.