If you’ve been diagnosed based on your lesions, physical examination and history, I don’t see the point in your having an LP. But regardless of that, an LP will only tell the neurologist that you do or don’t have Oligoclonal bands in your CSF. It won’t tell him/her what kind of MS you have.
Generally, people are assumed to have relapsing remitting MS unless there is pretty strong evidence that you have progressive MS. Which would be having symptoms which never remit and basically just get worse. So it’s a symptomatic thing rather than an evidence based decision. And tends to be something that is decided pretty much after some time has passed following your diagnosis.
So, most people are diagnosed, either with or without a lumbar puncture and are then started on a disease modifying drug (DMD). These are designed to reduce relapses and severity of relapses. If after a year or so, you’ve had no remission, it might be that the neurologist feels that actually you are progressive. Either Primary Progressive (having never had any remission) or Secondary Progressive (having passed through a phase of RR before diagnosis).
In your situation, I’d be querying the need for an LP. Either the neurologist is certain that you have MS now or they are not. The LP might make a diagnosis more secure, but not necessarily since only 80 to 95% of people have ‘O’ bands in their CSF. So if you had a negative LP, you’d probably still have MS. But you could ask your neurologist that. (Speak to his/her secretary?) and then get started on a DMD as soon as possible.