  In this paper we study the integral form of the lattice vertex algebra $V_L$.
We show that divided powers of general vertex operators preserve the integral
lattice spanned by Schur functions indexed by partition-valued functions. We
also show that the Garland operators, counterparts of divided powers of
Heisenberg elements in affine Lie algebras, also preserve the integral form.
These construe analogs of the Kostant $\mathbb Z$-forms for the enveloping
algebras of simple Lie algebras and the algebraic affine Lie groups in the
situation of the lattice vertex algebras.
