This paper is part of a larger project in which we systematically study the chemical abundances of Galactic and extragalactic post-asymptotic giant branch (post-AGB) stars. Lead (Pb) is the final product of the s-process nucleosynthesis and is predicted to have large overabundances with respect to other s-process elements in AGB stars of low metallicities. However, Pb abundance studies of enriched post-AGB stars in the Magellanic Clouds show the Pb overabundance is not observed. We used high-resolution UVES and HERMES spectra for detailed spectral abundance studies of our sample of 14 Galactic post-AGB stars. We do not find any clear evidence of Pb overabundances in our sample. Stars with T(eff) > 7500 K do not provide strong constraints on the Pb abundance. We conclude that the discrepancy between theory and observation increases towards lower metallicities. All objects, except IRAS 17279-1119, confirm the relation between neutron exposure [hs/ls] and third dredge-up efficiency [s/Fe], whereas no relation between metallicity and neutron exposure is detected within the metallicity range of our total sample (-1.4 < [Fe/H] < -0.2). The mild enrichment of IRAS 17279-1119 can probably be attributed to a cut-off of the AGB evolution due to binary interactions. To our knowledge, IRAS 17279-1119 is the first s-process enhanced Galactic post-AGB star known in a binary system and is a possible precursor of the extrinsic Ba dwarf stars. Lead-rich stars have yet to be found in post-AGB stars. extrinsic Ba dwarf stars. Lead-rich stars are yet to be found in post-AGB stars.
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