  We investigate the Lawson genus $2$ surface by methods from integrable system
theory. We prove that the associated family of flat connections comes from a
family of flat connections on a $4-$punctured sphere. We describe the
symmetries of the holonomy and show that it is already determined by the
holonomy around one of the punctures. We show the existence of a meromorphic
DPW potential for the Lawson surface which is globally defined on the surface.
We determine this potential explicitly up to two unknown functions depending
only on the spectral parameter.
