Context : This paper is part of a larger project in which we systematically study the chemical abundances of extra-galactic post-asymptotic giant branch ( post-AGB ) stars .
The aim of our programme is to derive chemical abundances of stars covering a large range in luminosity and metallicity with the ultimate goal of testing , constraining and improving our knowledge of the poorly understood AGB phase , especially the third dredge-up mixing processes and associated s -process nucleosynthesis .

Aims : Post-AGB photospheres are dominated by atomic lines and indicate the effects of internal chemical enrichment processes over the entire stellar lifetime .
In this paper , we study two carefully selected post-AGB stars : J051213.81-693537.1 and J051848.86-700246.9 in the Large Magellanic Cloud ( LMC ) .
Both objects show signs of s -process enhancement .
The combination of favourable atmospheric parameters for detailed abundance studies and their known distances ( and hence luminosities and initial masses ) make these objects ideal probes of the AGB third dredge-up and s -process nucleosynthesis in that they provide observational constraints for theoretical AGB models .

Methods : We use high-resolution optical UVES spectra to determine accurate stellar parameters and subsequently perform detailed elemental abundance studies of post-AGB stars .
Additionally , we use available photometric data covering optical and IR bands to construct spectral energy distributions for reddening and luminosity determinations .
We then estimate initial masses from theoretical post-AGB tracks .

Results : We obtained accurate atmospheric parameters for J051213.81-693537.1 ( T _ { \textrm { eff } } = 5875 \pm 125 K , \log g = 1.00 \pm 0.25 dex , [ Fe/H ] = - 0.56 \pm 0.16 dex ) and J051848.86-700246.9 ( T _ { \textrm { eff } } = 6000 \pm 125 K , \log g = 0.50 \pm 0.25 dex , [ Fe/H ] = - 1.06 \pm 0.17 dex ) .
Both stars show extreme s -process enrichment associated with relatively low C/O ratios of 1.26 \pm 0.40 and 1.29 \pm 0.30 for J051213-693537.1 and J051848-700246.9 , respectively .
We could only derive upper limits of the lead ( Pb ) abundance .
These upper limits show a possible very slight Pb overabundance with respect to heavy s -elements for J051213-693537.1 , while J051848-700246.9 shows an upper limit of the Pb abundance similar to [ hs/Fe ] .
A comparison with theoretical post-AGB evolutionary tracks in the HR-diagram reveals that both stars have low initial masses between 1.0 and 1.5 M _ { \odot } .

Conclusions : This study adds to the results obtained so far on a very limited number of s -process enriched stars in the Magellanic Clouds .
With the addition of the two stars in this study , we find an increasing discrepancy between observed and predicted Pb abundances towards lower metallicities of the studied s -process rich post-AGB stars in the Magellanic Clouds .
The more metal-rich J051213-693537.1 fits the theoretical Pb abundance predictions well , while the five other objects with [ Fe/H ] ¡ 1 , including J051848-700246.9 , have much lower Pb overabundances than predicted .
In all objects found so far , including the objects in this study , the C/O ratio is very moderate because of the enhancement of O as well as C. We find that all s -process rich stars in the LMC and SMC studied so far , cluster in the same region of the HR-diagram and are associated with low-mass stars with a low metallicity on average .
We corroborate the published lack of correlation between the metallicity and the neutron irradiation , while the neutron exposure ( [ hs/ls ] ) is strongly correlated with the third dredge-up efficiency ( [ s/Fe ] ) .
These correlations seem to hold in our Galaxy as well as in the Magellanic Clouds .