Let $L$ be an indefinite {\it non-unimodular} integral lattice. I am particularly interested in unimodular cases, such as $U\oplus A_2, U\oplus D_4$. Are there any general method to determine whether or not the orthogonal group $O(L)$ is a finite group?

I am aware of this similar question Automorphism groups of indefinite non-unimodular integer lattices The difference is, I am interested only in whether or not $O(L)$ is finite.