  This is the second article in a suite of articles investigating relations
between St\"{a}ckel-type systems and Painlev\'{e}-type systems. In this article
we construct isomonodromic Lax representations for Painlev\'{e}-type systems
found in the previous paper by Frobenius integrable deformations of
St\"{a}ckel-type systems. We first construct isomonodromic Lax representations
for Painlev\'{e}-type systems in the so called magnetic representation and
then, using a multitime-dependent canonical transformation, we also construct
isomonodromic Lax representations for Painlev\'{e}-type systems in the
non-magnetic representation. Thus, we prove that the Frobenius integrable
systems constructed in Part I are indeed of Painlev\'{e}-type. We also present
isomonodromic Lax representations for all one-, two- and three-dimensional
Painlev\'{e}-type systems originating in our scheme. Based on these results we
propose complete hierarchies of $P_{I}-P_{IV}$ that follow from our
construction.
