Why can't a lumbar puncture be used for someone who has a subdural haematoma?

For what purpose?: Subdural hematoma can not be diagnosed by lumbar puncture and there is the risk of brain herniation into the spinal canal and death if intracerebral pressure is increased due to sub-dural hematoma.

Herniation risk: When you remove spinal fluid during an lp, you lower spinal column pressure. If you have something in or around your brain that's increasing pressure within the skull (including blood), this could cause the brain to "herniate"-- to squeeze into places it doesn't belong to go from a high pressure area to a low pressure area. Herniation can be fatal, which is why we don't take the risk.

Risk of herniation: Because a lumbar puncture can cause downward brain herniation in a patient with increased intracranial pressure from a space occupying lesion in the brain such as a subdural hematoma.