You said 'good lyrics' which can be taken many ways (Intelligent, heartfelt, rational, deep, interesting, better-than-shitty). However, I still think this question has no answer; there is no such thing as an emo/screamo band that makes music with any lyrics worthwhile. The answer to your question is to find a new genre of music that doesn't completely suck.
blessthefall, motionless in white,atreyu, skillet, system of the down, woe is me,alesana, the word alive, underoath,bring me the horizon, black veil brides, in faith and fear, cold,korn,flyleafavenged sevonfold, the devil wears prada,chidos, abandon all ships, asking alexndria, hopes die last,
Eyes set to kill
Escape the fate
Bring me the horizon
Falling in reverse
Pierce the veil
The red jumpsuit apparatus
Blessthefall, alesana, hopes die last, scary kids scaring kids, red jumpsuit apparatus, rise against, black veil brides, the used, eyes set to kill, sleeping with sirens, funeral for a friend, the material, papa roach, silverstien, and versaemerge
In your opinion screamo sucks but to everyone eleaw who commented wjth bands they like it and some screamo bands do have MEANINGFUL and HEARTFELT lyrics
EXAMPLE Roses For the Dead -Funeral For A Friend
EXAMPLE Carolyn - Black Veil Brides
The Devil Wears Prada, Chelsea Grin, Whitechapel, Behemoth, Your Hidden Beauty, Get Scared, Avenged Sevenfold (not really 'screamo' but still good :D) A day to Remember, Silverstein, Of Mice and Men, Parkway Drive, Dance Gavin Dance
Motionless in White.
Avenged sevenfold - almost easy.
The Devil wears Prada.
The Devil Wears Prada
Escape The Fate
Black Veil Brides
My Chemical Romance
Goodie but oldie: Five Finger Death Punch - very awesome!
Lol I listen to every band that you just named:P
System of a down! All the way they are AMAZING!
Slip knot is supposedly one.
And falling in reverse
Bring me the Horizon