I assume you mean the E-W lake along Rt. 74 east of Paradox Lake. I stayed at the Eagle Lake lean-to a few years ago when my primary destination couldn't be reached due to flooded roads. I don't think you can call this a campground as there are no facilities of any kind (except the lean-to), there are no reservations, and access is only by boat. Motors allowed although I paddled.
The only access I know of is from the boat launch at the far west end of the lake (and S. of Rt 74). Parking & a sign in register there. You need to head east and then under Rt. 74. If high water, a tall boat (or people) might have a problem (I think you can pull over near the bridge & scout this out). I've heard of another boat access near the bridge, but never have seen it.
Paddle to the far NE end of the lake where it narrows. On the N. shore there is a picnic area and open woods with room for several tents. Back further off the lake due east is a lean-to. OK spot but I don't think it has a view of the lake. Hiking trail east from there goes to private property.
There are a number of homes/camps on Eagle Lake but I saw only limited boat traffic. Nice place but not a wilderness feel at all. I think there was road noise audible from the lean-to.