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
http://mathoverflow.net/questions/136338/automorphism-groups-of-indefinite-non-unimodular-integer-lattices
The difference is, I am interested only in whether or not $O(L)$ is finite.