If the Lincoln is anything like our forests in Wyo, then any flat ground anywhere near water with road access will be occupied. You can find peace and quiet on the forests, but not near any water that is near a road. I quit going there a long time ago.
My suggestion is to hike a reasonable distance,then camp and fish. The further you go the less intrusion you'll have, but just a mile will make a huge difference. Another suggestion if you go this route, don't wait too long into the afternoon to find a campsite. Finding a flat spot big enough for even a small tent can be a real problem what with rocks and brush. Also my pet peeve, any such spot will most likely have a dirty nasty fire ring right in the middle, so you have to pitch your tent in the rough ground. Here again if you move away from the water your chances of finding a nice campsite will improve.
I wouldn't be tempted to go without a tent. Even if the chances of rain are slim, the skeeters will drive you crazy. You don't have to have a $300 tent to crawl into for the hours of darkness. I used to use a little pup tent. It was fully screened, and it was way lighter than the expensive tents. Cost about $30 back when I was hike/fishing.
