If I have mask of foresight and move a lilia fae fawn to an enemy occupied bf and then play smoke and mirrors, will it trigger the mask of foresight for the swapped sprite and can I react to the mask of foresight with engarde to make the swapped sprite 9 might and then leaving a sprite from Likia move trigger?

Yes — the swapped-in Sprite triggers Mask of Foresight on its own, and you can play En Garde in response to that trigger.

Mask triggers anew for each unit that gains the attacker/defender designation alone during the Showdown (once per unit per combat — FAQ #11212, #5044). So after Smoke and Mirrors swaps Lillia out and the Sprite in, put Lillia's move-trigger on the Chain first, then the Mask trigger, then En Garde on top. Resolution order: En Garde first — the Sprite is still the only friendly unit at that battlefield, so it gets +2 (+1, then +1 alone) — then Mask's +1 resolves (it's locked in regardless of what joins later), and only last does Lillia's trigger play the new 3/3 Sprite there. That new Sprite does not trigger Mask since it doesn't enter alone.

Watch the math, though: the swapped Sprite ends at 6 Might (3 base + 2 from En Garde + 1 from Mask), not 9 — Mask gives +1 only once per unit per combat, so there's no second Mask trigger to stack. And if Lillia's token were allowed to resolve before En Garde, En Garde would only give +1 (Sprite ends at 5), so the trigger ordering above is what secures the full bonus.