  To analyze the absolute condition number of multivariate polynomial
interpolation on Lissajous-Chebyshev node points, we derive upper and lower
bounds for the respective Lebesgue constant. The proof is based on a relation
between the Lebesgue constant for the polynomial interpolation problem and the
Lebesgue constant linked to the polyhedral partial sums of Fourier series. The
magnitude of the obtained bounds is determined by a product of logarithms of
the side lengths of the considered polyhedral sets and shows the same behavior
as the magnitude of the Lebesgue constant for polynomial interpolation on the
tensor product Chebyshev grid.
