  Inspired by the two-parameter Macdonald-Cherednik deformation of the formulae
for non simply laced simple Lie algebras, we propose a two-fold refinement of
the partition function of the corresponding Chern-Simons theory on $S^3$. It is
based on a two-fold refinement of the Kac-Peterson formula for the volume of
the fundamental domain of the coroot lattice of non simply laced Lie algebras.
We further derive explicit integral representations of the two-fold refined
Chern-Simons partition functions. We also present the corresponding generalized
universal-like expressions for them. With these formulae in hand, one can try
to investigate a possible duality of the corresponding Chern-Simons theories
with hypothetical two-fold refined topological string theories.
