I’m not a medic, so bear with me! A lumbar puncture takes a small sample of spinal fluid which is then tested for abnormal proteins. This shows that the immune system has been at work in the central nervous system - they are looking for you testing positive for oligoclonal bands. So really, you are looking to test positive, not negative. BUT! It’s not a fool-proof test and is normally only used when a diagnosis of MS has not been confirmed by other tests, it just adds weight to your diagnosis. So if it comes back clear, there is still a chance you have MS.
If you would like a more ‘medical’ explanation, there is lots on this MS society website or MS Trust - just google. As for how long the results take, it really does depend! I called the hospital within a week as I couldn’t wait, lol. Sometimes your GP will also hear before you. Best thing to do perhaps is explain you would like to know the results as soon as possible and how can you find out. Get a telephone number and a clear idea of when you can call to find out. Sometimes you have to shout a little louder than everyone else!