I have an overnight connection coming up in Tokyo - arriving in NRT late afternoon on a Saturday and departing from HND the next day in the afternoon.
I will be staying at a hotel in Shinagawa which is close to the Shinagawa train station and therefore easy access to HND airport.

I read up on the recent opening of the rooftop onsen / hot spring facility at the Villa Fontaine Grand Hotel at Haneda Airport and I'm tempted to give that a try before my flight out of HND. My flight leaves from T3 and I understand there is a walkway that connects the hotel to the T3 Arrivals lobby.
To experience the onsen, I was thinking of checking out of my hotel in Shinagawa early AM, take the Keikyu train and aim to be at the onsen around 8:00, so I have enough time for a soak before checking-in in for my onward Lufthansa flight which leaves at 12:50 pm. The check-in for this flight won't open until 3 hours before departure.

My questions are :
1. Are there luggage storage facilities for those not staying at the hotel but just using the onsen on a casual basis ? The luggage storage at HND T3 to be closed, according to the Haneda airport website
2. How easy is the access from the Haneda Airport train station to the onsen considering I will have one large bag and a carry on ?
3. Their website mentions that the facility is closed once a month for inspection but couldn't find info online on exactly when they close. I emailed the hotel to find out but haven't had a response yet.

Thanks.