  In this paper, we construct a Lax pair for the classical hyperbolic van
Diejen system with two independent coupling parameters. Built upon this
construction, we show that the dynamics can be solved by a projection method,
which in turn allows us to initiate the study of the scattering properties. As
a consequence, we prove the equivalence between the first integrals provided by
the eigenvalues of the Lax matrix and the family of van Diejen's commuting
Hamiltonians. Also, at the end of the paper, we propose a candidate for the Lax
matrix of the hyperbolic van Diejen system with three independent coupling
constants.
