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.

The spell has no knowledge of cards chosen for other spells named Forgotten Lore.