I want to understand what's meant by "Lie type" in the paper "Character degrees and random walks in finite groups of Lie type" by Liebeck and Shalev, available here. Several theorems involve statements such as "fix a (possibly twisted) Lie type $L$'' (Thm 1.1).
What is a Lie type? Examples from the paper include things like $L = L_2$, $F_4$, or $^2F_2$. It is also clear that a Lie type has an associated Coxeter number $h$.
I'm not a finite group or Lie theorist, but I know that there is a connection to root systems. I understand these to be a certain kind of finite geometric/combinatorial object. Do root systems have some axiomatization such that they precisely correspond to Lie types $L$ of quasisimple finite group, as used in this paper? If the story is complicated as I suspect it is, efficient references would be helpful.