Each player on a team counts their Lore Shards separately. Both players must accumulate 20 lore, and a single player may exceed 20 lore while their teammate attempts to get to 20.  While both players must reach 20 to win, if one player on a team loses, the whole team loses. 

This format uses the multiplayer simultaneous turns rule outlined in the CR (see below). While players share turns and information, cards or effects in their deck, hand, play, inkwell, discard, and bag belong to the player who owns them within the game.

1.10.3. Some multiplayer game formats use simultaneous turns.

1.10.3.1. During a simultaneous turn, all players on the same team progress through the phases and steps of the game at the same time. During the Main Phase, the players can take any turn action they could take normally in any player order they wish. Players must complete one turn action in its entirety before moving to the next turn action.

1.10.3.2. If triggered abilities or effects are added to the bag by multiple players during a simultaneous turn, these triggered abilities or effects are added to the bag by the team as a whole, and the order in which they are resolved is chosen by the team. Otherwise, resolving follows the same rules found in section 8.7, “Bag.”