The likelyhood of LP getting added per Empower or the Tier of affixes getting added is based on the Uniques Rarity/LP Chance.
So uniques that you naturally find less with LP have much lower chance to get LP in the first place and if affixes are added they are usually alot lower tier.
For very low LP chance uniques I find the Nemesis system very weak. Which is ok, because its a chance and it won’t make the item “worse”.
For example Event Horizon (a uniques with incredibly low chance for LP): I put roughly 40 0LP ones into the Nemesis and only 3 came out with 1 LP, not a single one with 2LP, the rest mainly got T2 Affixes added on the first empower, which then got to T4 on the 2nd Empower.
For much higher LP chance uniques you will see 1LP much more common and also see 2LP more reliably.
In a sense the Nemesis system is much, much weaker for these kind of items, because even if a affix is added and it is the right one, you would be looking for, their tier for the most part is very low, most of the time not evne exalted.
Obviously this is an extreme case, but the kind of uniques that are hard to come by LP to begin with are the ones that are most chased for many builds.
If you take a little bit less extreme example, but still a “rare” unique (with somewhat low LP chance) you will see 2LP a bit more often, but still LP chance and affixes getting added are also relative to the items rarity/LP chance.