  The generic fiber of a Lagrangian fibration on an irreducible holomorphic
symplectic manifold is an abelian variety. Associate a polarization type to
such Lagrangian fibrations coming from polarizations on a generic fiber. We
prove that this polarization type is constant in families of Lagrangian
fibrations. Further, we determine the polarization type of K3^[n]-type
fibrations and conjecture that the polarization type should only depend on the
deformation type of the total space.
