Polymer-mediated lock-and-key assembly via depletion attraction is purely a shape-recognition process without any molecular bonding. Since the depletion attraction relates to osmotic pressure and excluded volume, the binding tendency in a dispersion of lock-and-key colloids can be controlled by adjusting the characteristics of polymeric depletants. In this work, dissipative particle dynamics accounting for explicit solvents, polymers, and multiple lock-key pairs are performed to investigate the influences of the polymer concentration, chain length, solvent quality, and chain stiffness. As the polymer concentration associated with osmotic pressure is increased, the binding free energy (E(b)) between a lock-key pair rises linearly and the binding fraction (θ(LK)) in the dispersion grows sigmoidally. Moreover, the increases in the chain length, solvent quality, and chain stiffness lead to the expansion of the polymer size associated with excluded volume and thus both E(b) and θ(LK) rise accordingly. However, E(b) and θ(LK) grow to be insensitive to the chain length for long enough polymer coils but still can be enhanced if the polymer becomes rod-like. As the solvent quality is varied, θ(LK) can be dramatically altered, although the radius of gyration of polymers is slightly changed.