Why does a person need a higher concentration of antibiotics with a brain infection then with a lung infection?

Blood Brain Barrier. There is a layer of protection around the brain that makes it harder for certain medications to get to the brain. If you need them to get there you have to use a higher dose.
BBB. Bbb= blood-brain-barrier. This physical structure (microscopic in scale) is what regulates and limits entry & exit of chemicals (including drugs) in the nervous system (cns). Hence the need for higher blood level of drugs to expect penetration of antibiotics (or other drugs) into CNS in adequate quantity.