Self-assembly of colloidal particles is emerging as a promising approach for producing novel materials. These colloidal particles can be synthesized with protrusions (lobes) on their surfaces that allow the formation of porous structures with a wide range of applications. Using Langevin dynamics simulations, we studied self-assembly in the binary mixtures of lobed colloidal particles with variations in their lobe sizes to investigate the feasibility of using dumbbell particles (with two lobes) as cross-linkers to increase the porosity in self-assembled morphologies. Each binary system was formed by mixing the dumbbell particles with one of the following types of particles: trigonal planar (three lobes), tetrahedral (four lobes), trigonal bipyramidal (five lobes), and octahedral (six lobes). We observed that the lobe size on each particle can be tuned to favor the formation of random aggregates and spherical aggregates when the lobes are larger and well-ordered crystalline structures when the lobes are smaller. We also observed that these polydisperse systems form self-assembled structures characterized by porosities higher than those of the structures formed by the monodisperse systems. These results indicate that the lobe size is an important design feature that can be optimized to achieve desired structures with distinct morphologies and porosities, and the dumbbell particles are effective cross-linking agents to enhance the porosity in self-assembled structures.