  We study the decomposability of a Lagrangian homology class on a K3 surface
into a sum of classes represented by special Lagrangian submanifolds, and
develop criteria for it in terms of lattice theory. As a result, we prove the
decomposability on an arbitrary K3 surface with respect to the K\"ahler classes
in dense subsets of the K\"ahler cone. Using the same technique, we show that
the K\"ahler classes on a K3 surface which admit a special Lagrangian fibration
form a dense subset also. This implies that there are infinitely many special
Lagrangian 3-tori in any log Calabi-Yau 3-fold.
