pL is a very strong promoter. For pL to work (this is the left promoter from bacteriophage lambda) you would need to also express the cI repressor (also from lambda) which controls this promoter as well.
You would need to clone the entire promoter plus the cI repressor (should be controlled by something) and ensure that a sigma factor from the new organism can recognize the pL promoter sequence.
When cI is expressed, it will bind to the operator next to the pL promoter sequence and prevents expression.
When cI is not expressed, the pL promoter expresses whatever it's supposed to express.
That way you can control expression using this promoter/repressor system.
