Starters are meant to create a higher yeast cell count and optimal yeast health. Shaking the container with the starter keeps the yeast in suspension and helps keep oxygen in the liquid.
Once fermentation has started in your primary, introducing more oxygen to the wort will promote oxidation of the finished beer. On the other hand "disturbing" the wort such as moving the container, or even rousing the yeast from the bottom is not bad. Your goal would be to do so by keeping oxygen out of the container though. So keeping the lid on is your best bet.
Aside from that disturbing the container you are fermenting in will cause the sediment on the bottom to become suspended again, which could be considered bad by many brewers who want clarity in their beer once bottling/kegging.