In a nutshell...

If you run Fire Control Systems on IG-88B with Heavy Laser Cannon, can you then shoot your primary weapon, spend target lock, reroll, re gain a target lock, miss the the attack, fire heavy laser cannon, spend target lock, reroll, re gain target lock, end attack?

Thanks in advance.

yes, though why you'd not fire with the heavy laser cannon for the first shot too, I'm not sure

To be correct, the TL from FCS is gained after an attack, not after spending the TL.

So the sequence would be: spend target lock, reroll, miss the attack, re gain a target lock, fire heavy laser cannon, spend target lock, reroll, end attack, re gain target lock

and if you still can't blow them away after all that... maybe it's time to change your dice.

I have intentionally tried to miss shots on a buzzsaw before to pickup TL, so maybe he wanted to intentionally miss the first attack.... but he had TL for the first shot already so I dunno.