You can not use the airside lounges in any of the other terminals. There is the Wings transit lounge landside in Terminal 3 (You will need to check if it is still open as a lot of places have closed) It is not easy moving between terminals at Manila as they all spread out. There is a bus that goes between the terminals but it is not very reliable, So it is probably easiest to get a taxi or use the Grab app.
Whether it would be worth doing it I am not sure. It should only take 10 to 15 minutes by taxi between T2 and T3 but Manila traffic can be terrible you can also have a long wait for a taxi.