What you are stating is India's version. China has their own. As I said, I have no means to verify one or the other. It is an extremely complex problem, for the reason that LAC, in Kashmir, is neither drawn on map, nor demarcated on ground.
Tawang is not a lake. It is a town and territory, which lies in India's state of Arunachal Pradesh (erstwhile NEFA). This is under India's control. This recent clash has occured on LAC bordering this territory.
You probably mean Pangong Tso (Lake), which lies across LAC, partly, in Ladakh (India) and, partly, in Aksai Chin (China).