Condensation of water from the atmosphere on a solid surface is an ubiquitous phenomenon in nature and has diverse technological applications, e.g. in heat and mass transfer. We investigated the condensation kinetics of water drops on a lubricant-impregnated surface, i.e., a micropillar array impregnated with a non-volatile ionic liquid. Growing and coalescing drops were imaged in 3D using a laser scanning confocal microscope equipped with a temperature and humidity control. Different stages of condensation can be discriminated. On a lubricant-impregnated hydrophobic micropillar array these are: (1) Nucleation on the lubricant surface. (2) Regular alignment of water drops between micropillars and formation of a three-phase contact line on a bottom of the substrate. (3) Deformation and bridging by coalescence which eventually leads to a detachment of the drops from the bottom substrate. The drop-substrate contact does not result in breakdown of the slippery behaviour. Contrary, on a lubricant-impregnated hydrophilic micropillar array, the condensed water drops replace the lubricant. Consequently, the surface loses its slippery property. Our results demonstrate that a Wenzel-like to Cassie transition, required to maintain the facile removal of condensed water drops, can be induced by well-chosen surface hydrophobicity.