A Lindlar catalyst is a popular heterogeneous catalyst that consists of 5 wt.% palladium supported on porous calcium carbonate and treated with various forms of lead and quinoline. The additives strategically deactivate palladium sites. The catalyst is widely used for the partial hydrogenation of acetylenic compounds in organic syntheses. Alkyne reduction is stereoselective, occurring via syn addition to give the cis-alkene. Even if it has been employed for about 60 years, there is a lack of molecular level understanding of the Lindlar catalyst. We have applied density functional theory simulations to understand the structure and the nature of the interplay between the multiple chemical modifiers in the Lindlar catalyst. Indeed, the poisons influence different parameters controlling selectivity to the alkene: Pb modifies the thermodynamic factor and hinders the formation of hydrides, while quinoline isolates Pd sites thus minimizing oligomerization.