  In this paper, we construct the additional $W$-symmetry and ghost symmetry of
two-lattice field integrable hierarchies. Using the symmetry constraint, we
construct constrained two-lattice integrable systems which contain several new
integrable difference equations. Under a further reduction, the constrained
two-lattice integrable systems can be combined into one single integrable
system, namely the well-known one dimensional original Toda hierarchy. We prove
that the one dimensional original Toda hierarchy has a nice Block Lie symmetry.
