I agree with Domenico. Since the pLysS plasmid encoded chloramphenicol resistance, inclusion of chloramphenicol will maintain selective pressure, without impeding transgene expression. Nonetheless, you can safely omit chloramphenicol if you are transforming this strain with an expression plasmid, since the rate of plasmid curing (spontaneous pLysS plasmid loss) is quite low. Note that if you were trying to propagate the strain for other purposes (for example, making competent cells), keeping selective pressure on would be recommended.
Chloramphenicol is a specific resistance of BL21 pLysS cells: if the plasmid you use to transform the cells is Kan or Amp resistant, you can use LB agar plates with only your antibiotic, it will be selective! If you're unlucky and your plasmid has Chloramphenicol resistance then you have to choose another E. coli strain.
So, to answer you questions, you won't need Chloramphenicol at all in your growth!
I agree with Domenico. Since the pLysS plasmid encoded chloramphenicol resistance, inclusion of chloramphenicol will maintain selective pressure, without impeding transgene expression. Nonetheless, you can safely omit chloramphenicol if you are transforming this strain with an expression plasmid, since the rate of plasmid curing (spontaneous pLysS plasmid loss) is quite low. Note that if you were trying to propagate the strain for other purposes (for example, making competent cells), keeping selective pressure on would be recommended.