Target opponent chooses a card in your graveyard. You may pay {G}. If you do, repeat this process except that opponent can't choose a card already chosen for Forgotten Lore. Then put the last chosen card into your hand.
The spell has no knowledge of cards chosen for other spells named Forgotten Lore.
You target an opponent when you cast Forgotten Lore. The opponent chooses a card in your graveyard as Forgotten Lore resolves. After that choice is made, you’re given the option to pay {G}. If you do, the targeted opponent must choose a different card, if there is one. (If there isn’t one, this part is skipped.) Then you’re given the option to pay {G} again. As long as you keep paying {G}, the process continues. As soon as you decline to pay {G}, the last card that was chosen by the opponent is put into your hand.