Correct me if I'm wrong. The order of events when using the HLC with target lock would be roll, downgrade crits, then use target lock, right? So if I roll blank, blank, eye and crit I would change the crit to a hit, then I could use my lock to reroll the other three dice and keep any crits I rolled?

As I understand it anything that says "immediately" on the card happens before anything else (unless that other effect also says immediately) but I like to be certain of things like this.

Correct me if I'm wrong. The order of events when using the HLC with target lock would be roll, downgrade crits, then use target lock, right? So if I roll blank, blank, eye and crit I would change the crit to a hit, then I could use my lock to reroll the other three dice and keep any crits I rolled?

Correct.

HLC does not refer to the act of rolling dice. It refers to the roll attack dice step of the combat sequence. After that step HLC triggers and changes to . After that modify attack dice proceeds as normal without triggering HLC for a 2nd time.

As I understand it anything that says "immediately" on the card happens before anything else (unless that other effect also says immediately) but I like to be certain of things like this.

There is a fair amount of disagreement regarding the meaning of "immediately". Which is not relevant for HLC.

Edit:

Regarding "immediately", there is the precedent that after an attack that does not hit, the non-immediate Vader resolves before the immediate gunner. Which does not help to solve the matter.

The "immediately" isn't really relevant. HLC triggers off the dice roll, in Step 2, before any other modification can occur. So there's nothing for it to compete with.