From my reading, no.

As you mention in the question:

This may come down to whether or not the Lucky roll counts as an "attack roll" itself or whether the "attack roll" was the original roll and the Lucky roll is some other type of roll.

Yes, this is the case. And Lucky is not an attack roll.

Lucky says:

Whenever you make an attack roll, an ability check, or a saving throw, you can spend one luck point to roll an additional d20. [...] You choose which of the d20s is used for the attack roll, ability check, or saving throw.

You don't make a new attack roll - you just roll an extra die and then choose which die to use for the attack roll. The Lucky itself is not an attack roll, as much as attacking with advantage doesn't let you make two attack rolls or two saving throws, it is one attack roll that has a "more complicated" math than just rolling. Until you roll the additional d20 from Lucky, you are in the middle of the attack roll (just as you would be, for example, if you were rolling with advantage and rolled one die first, took a break and then rolled the other - you are in the middle of the same attack roll). Portent specifically asks "before the roll", so you can't use it.

For another example, a damage roll consists of all the damage dice summed, e.g. 2d6. Adding an extra 1d6 does not make an extra damage roll, just an extra damage die.

Overchannel replaces the damage of the spell, not any other mechanics

The only thing that changes when you overchannel a spell is that instead of adding up the numbers on the damage dice, you use the maximum possible result. Most of the time this means there is no point to rolling the damage dice, but it doesn't say that you don't.

In Chaos Bolt's case, you'd roll damage as normal, using the type table and chaining mechanics as explained in the spell, but you'd substitute the rolled damage with maximum damage.

As an example, if you rolled 1, 2 (d8s), and 6 (d6), you would choose either acid or cold, you wouldn't jump to a new target, and you'd do 22 damage.