  In this paper we study the integral form of the lattice vertex algebra $V_L$
and the associated vertex group. 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 generalized 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.
