If Norra holds target locks on two different ships (having weapons engineer), can she spend a lock on one ship to use her ability to add a focus result to her attack, and spend the other target lock to attack a different ship with her advanced proton torpedos, giving her a 5 die + 1 focused die attack on said ship?

(The idea being that she uses the eye-to-hit ability of the advanced proton torps to convert her added focus die to a hit).

No:

When attacking or defending, you may spend a target lock you have on the enemy ship to add 1 result to your roll.

And the target lock on the advanced torp has to be on the ship you are attacking. And since you can't have same ship targeted twice, that means that's out. Check. Thanks.

No, this doesn't work.

Norra's ability specifically says the Target Lock you spend to gain an extra [eye] result has to be on the ship you're attacking (or defending against).

The definition of the "Attack (Target Lock):" header (Rules Reference p16, "Secondary Weapons") specifically says the Target Lock you use to satisfy the header condition must be on the defending ship.

The only weak point here is the lack of a clear citation saying that the Target Lock you spend for a secondary weapon attack that requires you to spend a Target Lock has to be the same one you used to satisfy the Attack (Target Lock) header, but the Secondary Weapons entry in the Rules Reference implies that, and I'd be comfortable ruling that way in a tournament setting.

Drop Weapons Engineer and add in Deadeye EPT and Recon Spec. Makes for a one trick ship, but will take a nice chunk out of any ship. It's also a 2 round setup.

Round 1: Target Lock

Round 2: Focus x2, spend target lock for Norra's ability, Focus for Torpedo's, then Focus for hits. It's 4 hits guaranteed once.

And the target lock on the advanced torp has to be on the ship you are attacking. And since you can't have same ship targeted twice, that means that's out. Check. Thanks.

If you're flying with Shara Bey this would work wouldn't it? You spend Bey's lock to fire and Norra's lock to add the focus die for six die total.

Yep, it would work fine with Shara.

E: or Deadeye and RecSpec, potentially. But you'd have to TL in a previous round.