Baby Lake public or private?

Does any one have any information regarding Baby Lake (just south of Honnedaga Lake). Specifically looking for whether or not this is public or on the Adirondack League Club property and is private.



Any information would be great as I haven't been able to find much searching google other then it seems the ALC southern boundary line cuts off the northern most tip and satellite imagery does show a dock of some sort on the northern end of the lake.



Thanks in advance!