"Augment Lucky Value" is affected to mods tier?

I am enjoying the harvest content in this league. But there's something I don't really understand in this league that's called "Lucky Value." Does Lucky Value in "Agment an item with a new XXX modifier with Lucky values" affect the tier of the new XXX modifier?

No. It only affects the values that get rolled after the tier is determined. Lucky just means that it rolls twice and takes the better value of the two, but still within the range for whatever tier of the mod was already rolled.

Think of it as a targeted Divine orb.

No.
Lucky applies only to the actual value, not the tier.

Lucky applies to a roll with a minimum or maximum outcome, like an attack or a value for a modifier. Instead of just do a roll and go with that that roll says, the roll is done twice and the best outcome is chosen. In other words, if you should roll a Lucky 46-48 and the two rolls are (48,46), then 48 is chosen because is the highest.
Similiarly, an unlucky roll works the same way but applies the worst outcome (in the example above it would apply 46 because the lowest).
Its effect are most perceived when going with lightning because of its high variance in damage (10%-190% instead of the usual 80%-120% of other damage), or with modifiers that have a very big gap between minimum or maximum - though there aren't much of them among modifiers for rare items.

First, a tier is chosen. The chance for a T10 is the same for a T1 (if iLvl is right).
Then, the value is rolled twice and the best outcome is the new value for that Tier

In other words, Augment with new modifier with lucky value is just a half-hearted promise that whatever you will roll it will be the best of its world