From my experience, they only really let you bring in a clear water bottle and any other accommodated items, as well as a sticky note with your LSAC log in information on it. You likely can keep it in a locker at the testing center, but I doubt they will let you bring the coffee in with you as you actively take the exam. It may be different based on your testing center, so I would suggest giving them a call and asking beforehand so you have a better idea!