I read it an interview once, or was it a documentary? but I know I've seen it before.
But they said it's mostly based on how which part of the song goes with each member. Like how the song would sound if Tomomi sang this part or if Haruna, or if this part is good for Mami or Haru to sing. It's also about the song itself, based on the mood or tone of the song , the decide who will get to sing the most or the least. That's what's so good about Scandal songs because they take advantage of vocals provided by the members.
For example most all Haruna songs are serious, deep, slow, heavier, rockier, dark or mature: Burn, Weather Report, Emotion, Awanai, while most Tomomi songs, are cheery, poppy, romantic, sad, light hearted, upbeat, :houkago 1H, bitter Chocolate, Nai nai night, kill the virgin, Very special ( Tomomi doesnt have that many solo songs, so ive named songs she mostly sanged in) And if it's a Haru /Timo song, it's a bit of both characteristics, just to add some contrast.
As for if the lyricist sings the song, ehh not really...kinda.
Sometimes the songs where the members have no credit in: Koe, Nanka buttobase, Right Here, 24 jikan plus no yoake Mae, and cover songs. haves to rely on the tone / lyric view of the song to choose a vocalist. Sometimes the lyricist, whether the member, choose or say they like so and so to sing the song /part. So you see it's mostly about tone, mood, and style to choose who sings what in a song. If not they go through the song to see which part would fit best for what member.
I hope this answers your question and that you understand what I'm trying to get at. There is either a documentary or an interview that talked about how they decide the vocalist. Sorry if I can't tell you which one it was, but it was around 2010-2011 ish where it came out.