Let $L$ be a lattice associate to the Dykin matrix of type $E_{8}$. I would like to understand involutions of $L$ and their invariant $L^{+}$ and coinvariant lattice $L^-$ (I think they are isomorphic). I am sure that this has been studied in some literature. I would appreciate it if anyone could let me know the classification or some reference.

Any comments are welcome.