Lead (Pb) is predominantly produced by the slow neutron-capture process (s process) in asymptotic giant branch (AGB) stars. In contrast to significantly enhanced Pb abundances predicted by low-mass, low-metallicity AGB models, observations of Magellanic post-AGB stars show incompatibly low Pb abundances. Observations of carbon-enhanced metal-poor (CEMP) stars whose s-process enrichments are accompanied by heavy elements traditionally associated with the rapid neutron-capture process (r process) have raised the need for a neutron-capture process operating at neutron densities intermediate to the s and r process: the so-called i process. We study i-process nucleosynthesis with single-zone nuclear-network calculations. Our i-process models can explain the heavy-element abundance patterns measured in Magellanic post-AGB stars including their puzzlingly low Pb abundances. Furthermore, the heavy-element enhancements in the post-AGB and CEMP-i stars, particularly their Pb abundance, allow us to characterize the neutron densities and exposures of the i process that produced the observed abundance patterns. We find that the lower-metallicity CEMP-i stars () have heavy-element abundances best matched by models with higher neutron densities and exposures (τ > 2.0 mbarn-1) compared to the higher-metallicity post-AGB stars (, τ < 1.3 mbarn-1). This offers new constraints and insights regarding the properties of i-process sites and demonstrates that the responsible process operates on timescales of the order of a few years or less.