Yes it is hotel dependent, and some hotels will charge fee for extra persons in same room. However, I've not had any problem with 2 adults plus teenage daughter (no extra 3rd person fee either) into lounges in St. Regis Beijing, Le Royal Meridien Shanghai, Westin Chosun Seoul, Sheraton at the Park Sydney. I had to pay 3rd person fee for daughter, which then included breakfast at Sheraton Grande Sukhumvit Bangkok, and Renaissance Phuket.

Grand Hyatt Taipei would not allow 2nd person into lounge if the person is not registered in the room. I could not bring a colleague into the lounge. Other hotels in China did not even question.

Are you booking 2 rooms or 1 room with 4 adults? Teenagers are considered adults.