Synced turret instructs you to spend a target lock. Would this card work with deadeye so you would only need to spend a focus instead?

The card actually says that you can treat "Attack (Target Lock):" as "Attack (Focus):", and if the attack requires you to spend a target lock you can spend a focus token instead.

So yes, it works for Synced Turret, so if you get someone in arc then you get full modifiers (roughly) from the Synced Turret Re-rolls and the focus token.

Synced Turret does not instruct you to spend a target lock. It merely requires you have have one in order to initiate the attack. And yes, that can be circumvented with Deadeye.

With Synced Turret, you must have a target lock on the defender, but there's zero requirement to spend that lock. And as @InquisitorM stated, Deadeye can be used, which means any target is now possible (although a primary arc target is preferable with Synced Turret).