This paper presents major improvements in the efficiency of the so-called Radical-Like Polymerization (RLP) algorithm proposed in "Polymer chain generation for coarse-grained models using radical-like polymerization" [J. Chem. Phys. 128 (2008)]. Three enhancements are detailed in this paper: (1) the capture radius of a radical is enlarged to increase the probability of finding a neighboring monomer; (2) between each growth step, equilibration is now performed with increasing the relaxation time depending on the actual chain size; (3) the RLP algorithm is now fully parallelized and proposed as a "fix" within the "Lammps" molecular dynamics simulation suite.