In complex socio-technical systems such as construction projects, the lean emphasis on waste reduction can contribute to the depletion of necessary slack for managing unexpected variability. This risk is amplified by the absence of a solid lean theory on slack and on how to manage the trade-off between slack and efficiency. Furthermore, lean focuses on managing slack in terms of time and inventories. Thus, a broader approach that accounts for a wide variety of slack resources is necessary. In this paper, the complexity science's and lean's views of slack are laid down and compared based on eleven criteria. Commonalities and conflicts between both approaches are identified, and proposals for future research related to slack management in lean complex systems are presented.