Agree with malarneela above.
In the USMLE exam you have to make sure first that it's a case of meningitis (fever, vomiting, nuchal rigidity, rash, ...etc).
If this is correct then give the IV antibiotic shot immediately and then arrange for LP and/or CT scan.
If there are signs of raised intracranial pressure (papilledema, headache, respiratory compramise, cushin triad, ...etc) then don't do the LP, instead order CT scan.
If there are signs that make the diagnosis of meningitis questionable then do CT first before doing anything else.
PS- thank you Sabio, this is a great topic to discuss