Been there twice on a touristy trip with visitors from Europe. Both times the only boats I saw were the ones they use to ferry tourists from the first lake to the other side so they can walk up to the second lake. Not seen anyone fishing there either.
It is a rather nice trip, I remember while we were in the boat, my grandson referring to the surrounding hills as "broccoli mountains" (because they are incredibly green). The last bit of the road to get there is fairly steep though, and parking is a fair bit higher than the lake itself, so you need to be ok with walking down a hill and back up again.
Kidding aside though, not sure but I think it might well be the case that the entire area is protected and that fishing is prohibited.