I did international transfer in ICN last month. The transfer was quick at that time. Took me 2 minutes to pass the security (not passing the immigration). The Asiana Business Class lounge is located upstairs. Make sure that you look for the OZ lounge signs. I think they recently relocated to a new location so not all the maps have been updated. I went to the old location when I was there. The new one is nearby though, so don't worry. The lounge has plenty of shower rooms (6 I think) and plenty of space. The food was just ok. The variety was a bit limited in my opinion.

So, 3 hours, logically should be sufficient. The international transfer is the key. Just go there quickly before the queue builds up.