Directly below the colosseum on the surface, central Hyrule northeast of the Great Plateau, iirc.
Also, if you leave, you can come back later and it saves how many Lynels you've killed (unless there's a blood moon). I know this, because I broke my master sword on Every Single Lynel and had to leave for 10 minutes so it could regen
Also, the last silver lynel broke all but one of my shields, and it was Badly Damaged