According to this data sheet, the genotype of the strain RosettaTM(DE3)pLysS is F- ompT hsdS (r- m-) gal dcm (DE3) pLysSRARE (CamR).
This strain carries certain tRNA genes on the same plasmid as the LysS gene, and these tRNAs boost expression from genes containing rare (in E. coli) codons. The plasmid encodes chloramphenicol resistance (CamR).
If you have a protocol that suggests growing your strain under kanamycin selection then presumably you have an additional plasmid present which carries your gene of interest. Then, as the accepted answer says, you are selecting positively for the correct strain.
I don't know how stable the pLysSRARE plasmid is, but I would have expected that you should also maintain selection for chloramphenicol resistance.