If you have the gear which gives 1 might when you attack or defend alone. And you have a sprite at base and a unit which creates a sprite in the location it moves from. Let's say you have that unit defending. Reveal a tide turner to move it to base and move the sprite to the battlefield. But that also means a new sprite is added when it is moved, does one soirtr get the solo attack buff before the second sprite is generated by the move?

Yes — the sprite that arrives first gets the +1 from Mask of Foresight, and its trigger fires before Lillia's trigger creates the second sprite.

Here's the timing: the sprite gains its Defender designation during the Cleanup after the swap action resolves — while Lillia has already left and her "when I move" trigger is still pending. Alone at that moment, the sprite satisfies "defends alone," so Mask's trigger fires and is locked in; Lillia's trigger resolving afterward to spawn sprite #2 doesn't undo it. Sprite #2 itself gets no Mask trigger, since it's designated while sprite #1 is already there (FAQ #11212).

One mechanical catch: a single Tideturner only swaps itself with one unit you control, so it can't literally move Lillia out and bring the base sprite in at once. If Tideturner swaps itself with the sprite while Lillia stays, the sprite isn't alone and gets nothing. The "Lillia out, sprite in" line needs a swap that actually relocates Lillia (e.g., Smoke and Mirrors) — if you swap Tideturner for Lillia instead, it's Tideturner that's designated alone and gets the +1.