I thought the whole point of the arrival lounge was for passengers to use it on arrival, even international flights? The eligibility criteria explicitly calls out international passengers. The location of the HND arrival lounge is listed as "Haneda Airport Terminal 2 Domestic Departure Lobby," so couldn't OP just get through customs/immigration and go to the departure lobby?

https://www.ana.co.jp/en/jp/guide/lo...rrival-lounge/