  Context: This paper is part of a larger project in which we study the
chemical abundances of extra-galactic post-AGB stars with the ultimate goal of
improving our knowledge of the poorly understood AGB third dredge-up mixing
processes and s-process nucleosynthesis. Aims: In this paper, we study two
carefully selected post-AGB stars in the LMC. The combination of favourable
atmospheric parameters for detailed abundance studies and their known distances
make these objects ideal probes of the internal 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 perform detailed elemental abundance
studies. Additionally, we use available photometric data to construct SEDs for
reddening and luminosity determinations. We then estimate initial masses from
theoretical post-AGB tracks. Results: Both stars show extreme s-process
enrichment associated with relatively low C/O ratios of about 1.3. We could
only derive upper limits of the lead (Pb) abundance which indicate no strong Pb
overabundances with respect to other s-elements. 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 Msun. Conclusion: This study adds to the
results obtained so far on a very limited number of s-process enriched post-AGB
stars in the Magellanic Clouds. We find an increasing discrepancy between
observed and predicted Pb abundances towards lower metallicities for all
studied Magellanic Cloud post-AGB stars found so far, as well as moderate C/O
ratios. We find that all s-process rich post-AGB 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.
