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This is the second article in a suite of articles investigating relationsbetween St\"{a}ckel-type systems and Painlev\'{e}-type systems. In this articlewe construct isomonodromic Lax representations for Painlev\'{e}-type systemsfound in the previous paper by Frobenius integrable deformations ofSt\"{a}ckel-type systems. We first construct isomonodromic Lax representationsfor Painlev\'{e}-type systems in the so called magnetic representation andthen, using a multitime-dependent canonical transformation, we also constructisomonodromic Lax representations for Painlev\'{e}-type systems in thenon-magnetic representation. Thus, we prove that the Frobenius integrablesystems constructed in Part I are indeed of Painlev\'{e}-type. We also presentisomonodromic Lax representations for all one-, two- and three-dimensionalPainlev\'{e}-type systems originating in our scheme. Based on these results wepropose complete hierarchies of $P_{I}-P_{IV}$ that follow from ourconstruction.

Systematic construction of non-autonomous Hamiltonian equations of Painlev\'{e}-type. II. Isomonodromic Lax representation