Experimentally, when an E. coli bacterium already has a prophage integrated into its chromosome, another

Question:

Experimentally, when an E. coli bacterium already has a λ prophage integrated into its chromosome, another λ phage cannot usually infect the cell and establish the lysogenic or lytic cycle. Based on your understanding of the genetic regulation of the λ life cycles, why do you think the other phage would be unsuccessful?