Classically, L is not an operator, so you cannot define a commutator. You can show that {L_{i}, L_{j}}=ε_{ijk}L_{k}. I don't know if that's what you meant by saying "Classically". If so, just write out L_{i} in terms of q_{i} and p_{i}. If you write the correct expression for it using Levi-Civita symbol and apply definition of Poisson bracket, it should be a trivial matter.
Yes, exactly. Thank you very much. Using square brackets may be confusing in classical mechanics. I figured out to make this with levi civita symbol. But there is another problem I have now. if I replace the L_{i} with some general vector V_{i}, it should still be hold {V_{i},L_{j}}=ε_{ijk}V_{k} how should I constract a general V vector?