HND-LHR
I used this service last summer and stayed the night before at the Tokyu hotel at Domestic T2. Although the HND website says the free shuttle bus to the international terminal doesn't start until 04:54 (a bit close for comfort) the hotel were advertising two earlier departures (sorry don't recall the exact time!) the second of which was more than adequate to arrive in good time for the flight.
I echo the sentiments that the food was only just being put out in the lounge, and the JAL FCL doesn't open until around boarding time!