Lapis has a fucked up information filter, and intakes all information. This leads to him being able to read extremely quickly, and retain all information he receives indefinitely.
He is the living encyclopedia.
Euclase has a fucked up pattern recognition ability, and can easily calculate highly complex numerical calculations within a short period of time. This leads to him being able to do accurate weather predictions and also lunarian predictor.
He is the living calculator.
Both of them are highly skilled at emotional manipulation.
This would have been perfectly balanced, if it weren't for the fact that Lapis is significantly more beautiful than Euclase, and due to having a broader field of expertice (he knew pretty much all the information available to the gems from the library) his ability is at first glance more useful to the other gems.
Things you can ask Lapis:>What are the characteristics of the haematocephala calliandra>Can you tell me about every discovered class of jellyfish and their individual life cycles>Can you tell me the chemical and structural composition of [any gem]>Can you explain to me how to do this part of my homework?>Can you tell me how to manipulate people (Lapis will happily tell you)
Things you can ask Euclase>what will the weather be like tomorrow (literally answerable by looking at the sky)>what was the weather like 37400 days ago? (who the fuck cares?)>what's the likelihood of moonies killing me today aka. what's the weather like today? (literally answerable by looking at the sky)>what colour scheme is your hair? (literally answerable by looking at the sky)>Can you tell me how to manipulate people? (Euclase will refuse, as he only manipulates for himself)
On top of this, Euclase's hair looks like the daytime sky, and daytime means moonies, and moonies mean danger. Meanwhile Lapis' hair looks like the sky at night, and nighttime means safety, relaxation, comfy card-games, and sleep.