There's a simple criterion when the lattice contains two copies of the hyperbolic plane: you look at the length of the vector and its image in the discriminant group of the lattice. Gritsenko, Hulek and Sankaran mention it here http://arxiv.org/abs/0810.1614 but the result goes back to Eichler (they refer to it as the Eichler criterion). If you're working with the Beauville form, then all known Hyperkahlers satisfy the hyperbolic condition.

There's a simple criterion for equivalence of two vectors in a lattice if the lattice contains two copies of the hyperbolic plane: you look at the length of the vector and its image in the discriminant group of the lattice. Gritsenko, Hulek and Sankaran mention it here http://arxiv.org/abs/0810.1614 but the result goes back to Eichler (they refer to it as the Eichler criterion). If you're working with the Beauville form, then all known Hyperkahlers satisfy the hyperbolic condition.