  Every isometry s of a positive-definite even lattice Q can be lifted to an
automorphism of the lattice vertex algebra V_Q. An important problem in vertex
algebra theory and conformal field theory is to classify the representations of
the s-invariant subalgebra V_Q^s of V_Q, known as an orbifold. In the case when
s is an isometry of Q of order two, we have classified the irreducible modules
of the orbifold vertex algebra V_Q^s and identified them as submodules of
twisted or untwisted V_Q-modules in [Bavalov-Elsinger]. Here we calculate their
quantum dimensions and fusion products. The examples where Q is the orthogonal
direct sum of two copies of the A_2 root lattice and s is the 2-cycle
permutation as well as where Q is the A_n root latice and s is a Dynkin diagram
automorphism are presented in detail.
