You have to have both the pL promoter as well as a second system of the cI repressor which controls the pL promoter. When the cI repressor is expressed it will bind onto the operator region of the pL promoter and prevent expression. When the cI repressor is not expressed it can't bind to its operator and the pL promoter (which is very strong) can express whatever gene it is upstream of. So you need to have both for transcriptional control. you don't need the rest of the phage!
