Should lumbar puncture be performed on my infant?

It depends. A lumbar puncture (LP) or spinal tap is a method for obtaining a sample of cerebral spinal fluid (csf). CSF is the fluid that surrounds the brain and spinal cord. An LP is usually done a part of a 'septic workup', in order to see if an ill person has meningitis. If your infant does have meningitis, it is important to know what is causing the infection and how best to treat that infection.
Ask your doctor. Only your infant's doctor can determine this. If your doctor needs to diagnose an infection in your infant and has recommended a lumbar puncture, you should follow their advice.