The integral form of VOA was well-studied by Dong and Griess for the finite auotmorphism group of VOA. We will show that the general divided powers of vertex algebras of lattice types preserve the integral forms spanned by Schur functions indexed by colored partitions. This provides an analog of Kostant's Z-forms and Lusztig's q-Z-form for lattice types VOA. We also show that the Garland operators preserve the integral forms.