Disney hotels are strict about not allowing you to complete check in until 3PM. My understanding is that you will not be allowed to use anything at the hotel including the lounge at that time.
If you drop off your luggage at the hotel as a pre-check in, they may even delay your check in completion time until 4:30PM or 5PM.
If you want a lounge, my recommendation is to stay at the Sheraton. I've checked in early plenty of times there and their lounge is the best of the hotels in the area. The Hilton should also let you check in early but I've never arrived in the morning for the Hilton. Just be aware that they probably won't let you into the lounge until breakfast is completed and there's a risk that they won't have a room available yet if you arrive super early.
My backup plan for when I want to rest but am afraid of not being able to check in is to get a private room at manga cafe like a kaikatsu club. But since you're planning to go to the Tokyo Disney area, there won't be any nearby if you get to your hotel and you can't access your room or the lounge yet. You'd have to go back to Tokyo station or East to Kahin-Makuhari.