Does Vex - Apathetic counter Lillia's ready sprites?

No, Vex, Apathetic does not counter the Sprite token created by Lillia, Fae Fawn's ability, but it will interact with it.

Explanation

To clarify the interaction:

1. Lillia's Ability: When Lillia moves, her ability plays a 3 [M] Sprite token. Because Lillia's ability uses the word "play," it fulfills the trigger condition for Vex, Apathetic ("When an opponent plays a unit...").
2. Interaction: As established in RiftJudge FAQ #8758 and RiftJudge FAQ #9485, tokens created by card effects that use the word "play" trigger Vex's ability.
3. Result: When the Sprite token enters the battlefield, Vex's triggered ability will resolve. The Sprite token will be Stunned and will gain the restriction that it cannot move for the remainder of the turn.

Why it is not a "Counter"

In Riftbound, Countering (Rule 425) specifically refers to negating the playing of a card or the activation of an ability, which clears that item from the chain and prevents it from doing anything.

Vex's ability does not Counter Lillia's ability or the playing of the token; instead, it waits for the token to enter the battlefield and then applies a Stun effect to that unit. The Sprite token still successfully enters play, but it arrives in a Stunned state.