If I have a Mask of Foresight on board, I have a Lillia on BF defending alone and a Sprite in base. Lillia will get the +1 from Mask first. Then, if I Smoke and Mirrors to swap locations of Lillia and the Sprite in base, could the Sprite in base get the Mask bonus before the move trigger resolves or does the closed state from the move trigger prevent that?

Yes, your Sprite will receive the +1 Might bonus from Mask of Foresight.

According to the official RiftJudge FAQ #10888, because the "alone" condition for the Sprite is met when it enters the location during the showdown, it triggers the Mask of Foresight anew. The bonus is applied to the unit that satisfies the "alone" condition at the moment it is designated or enters as an attacker or defender.

Detailed Sequence

1. Start of Combat: Lillia, Fae Fawn is designated as a defender alone at the battlefield. This triggers Mask of Foresight, which targets Lillia.
2. Playing Smoke and Mirrors: You play Smoke and Mirrors to exchange the positions of Lillia and the Sprite.
3. Triggered Abilities:
   • Lillia's Ability: When Lillia moves from the battlefield, her ability ("When I move from a location, play a 3 [S] Sprite unit token with [Temporary] there") is added to the chain.
   • New Trigger: As the Sprite enters the location alone during the showdown, the Mask of Foresight triggers again for the Sprite.
4. Resolution: You may order the resolution of these triggers. As clarified in FAQ #10888, the Sprite becomes the new target for the Mask of Foresight trigger, and once the trigger resolves, the +1 Might bonus is applied to the Sprite.

Key Rules

• Trigger Timing: The condition for "attacking or defending alone" is checked when units are designated or enter the battlefield at a location (Rule 460).
• Targeting: The bonus from Mask of Foresight applies to the specific unit that triggered the condition. When the Sprite replaces Lillia, it creates a new "alone" state, allowing it to trigger the Mask of Foresight itself.
• Stacking: Playing a card during a showdown creates a [Closed State] chain, but this does not prevent the resolution of triggers placed on the chain. You may resolve the Sprite's Mask trigger after the exchange to ensure it receives the bonus.

Note: I could not fully verify this ruling against the retrieved rules.