If I play Rampage on my unit with 6 might, against an opponent's lilia. And they play smoke and mirror to swap their lilia with their sprite. Would rampage deal damage to the lilia or the sprite?

Rampage deals the damage to Lillia, not the Sprite — your target was locked in when you played the spell, and Smoke and Mirrors only changes which units are where, it doesn't retarget Rampage.

Rampage's text has no "at a battlefield" or "same location" clause (compare Facebreaker's "at the same battlefield" or Bellows Breath's "at the same location"), so Lillia stays a legal target even after she moves to Base — Base is a board zone, so the targeting relationship is never severed (Rule 359.3.e.3). On resolution Lillia deals 3 to your unit and your unit deals 6 to Lillia, which kills her; the swapped-in Sprite, and any Sprite Lillia's move trigger makes, takes nothing.

Caveat: if the card did require the two units to share a location, the swap would make it whiff on both. Rampage doesn't print that, so the damage still lands on Lillia at Base. Also note this is spell damage, not combat damage, so nothing heals until the next Combat Cleanup or end of turn.