I am not the flight log expert so I can't comment on where it crash landed, I think
@sar104 and
@slup already answered this. I would theorize myself that it's possible it bounced on impact and could have bounced into the lake. Maybe unlikely, but who knows, anything is really possible.
My main point here is that is crash landed only a few hundred feet from where you were operating from, and there's only 3 or 4 trees there. It should in theory only take 5 minutes to look under those trees. If it's not there;
1. Someone stole it.
2. It bounced into the lake.
3. Its stuck in the tree somehow.
4. An animal carried it off.
If I was in your situation I would probably buy a wetsuit, life jacket, and a snorkle and search the lake at least 10ft from the shoreline in the area of those trees.
But again I am not the expert here, maybe one of the other experts can tell you that it's definitely not in the water.