Syrio initiates and wins the challenge, triggering his return to the shadows ability, but opponent plays A Lanister Pays his Debts.

Which effect takes precedence?

I assume the first player chooses?

The answer depends on which player has the first opportunity to respond. Since the challenge resolution is a framework action, the First Player has the first opportunity to respond.

Can you clarify that answer?

Syrio is when you win the challenge, return him to shadows. A Lannister always pays his debts, is after losing a challenge opponent must kill a character.

So you don't have to respond at all as the Syrio player his effect is default. The Lannister player has to choose to play his effect.

Does this mean Syrio always takes precedence?

Both the event and Syrio's ability are "Responses", which means playing them is automatic. Syrio does NOT automatically return to shadows, Syrio's controller must choose to trigger that Response after the challenge is done, just like the Lannister player must choose to play his event.

The First Player will have the first opportunity to play a Response after the challenge is over, followed by the player to his/her left. If First Player is Syrio's controller, Syrio will most likely live (as that player will most likely choose to return Syrio to Shadows as the first Response). If First Player is the Lanni player, Syrio will probably die.

Make sense?

Well, Andy beat me to the punch. An important thing to note: If you are the controller of Syrio and trigger a different response (Say Make an Example, if you'd counted 8 STR in the challenge) at your first opportunity, your opponent then has an opportunity to trigger a response and make Syrio Moribund: Dead PIle with the event before you get your 2nd opportunity to respond and use his ability. So, it would behoove you to trigger Syrio at your first opportunity.

Thanks guys, that is what I thought.

From what I gather, each succeeding response would happen in order. So first player gets a response, then second, then perhaps the first again if possible and so on?

Yeah, keep triggering those responses until all players consecutively pass.