At rest, or very light exertion levels, your body will burn almost exclusively fat for fuel. Even if it were true that your body burned any existing carb first, a whole lemon probably has about 5g carbs if you ate the entire fruit. Your body will burn nearly 100 calories at rest. If you divide that lemon water out over 12 hours, you have about 1.5 calories per hour of carb being ingested through lemon water. Even if you did burn the carb first you can see it would make no difference.
Nothing to worry about. Enjoy the lemon water, it's not hurting your fat burning in any way.