Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let (Γ, ⊥) denote the free orthogonality monoid over (X, #). Let C0(Γ, ⊥) be the subset of C(Γ, ⊥), consisting of all closures of bounded orthogonal sets. We show that C0(Γ, ⊥) is a suborthomodular lattice of C(Γ, ⊥) and we provide a necessary and sufficient condition for C0(Γ, ⊥) to carry a full set of dispersion free states.