Lakewater geothermal system
OK, sounds like most, if not all of the environmental and legal crap is a non-issue.
Next: OK so the lowest temperature you measured was 36F, but what about the highest temperatures in the summer? You will be trying to reject heat into the water in summer, so the idea is to try to locate the geo-exchange pipes as deep as possible to get the coolest surrounding water in summer as well. Conversely, in the wintertime, when you want to suck heat out of the lake, you want the geo-exchange pipes in non-freezing water that will be as warm as possible. Normally in winter the top surface depths of the water in a lake get colder than the deeper water. The thermocline level in the lake is what determines the depth at which the deeper water usually stays at around 39F year round. The depth of the thermocline varies with season and wind/wave action. In an ideal situation, the geo-exchange loops want to be below the thermocline so you can design the system for a more or less constant water temperature condition.
Shallow geo-exchange loops can be used, but they have to be sized for the worse case - the local water temperature in summer when you are trying to reject heat to the water, or winter, when you want to take heat from the water. If the lake is generally fairly shallow and there isn't enough depth near you to make use of the thermocline, you are in risky territory due to the lake water temperature fluctuations you will have to design for. This may double the size of the geo-exchange coils. The "general" (and I mean "general"!) rule of thumb is that you'd need about 200 feet of geo-exchange tube length per ton of cooling (or per 12,000 Btuh of heating). Depends which is the biggest load - do you need more cooling than heating? Or is the heating load what the heat pumps will be sized for?
The "200 feet" rule applies for just plain length, even if the tube was all coiled up. The actual tube length, size and configuration is location specific and installation-specific, so your local condition may dictate more , or less tube length per ton, depending on the load profile, energy balance, and water temperature conditions from season to season.
Closed loops are better..
Pond loops can be a real problem if water level drops or algee develops.An open loop should be min. of 15' if coiled and 10' lateral line loop.
I would suggest that you find a Geo-Thermal contractor in your area,and do research of climate of your area.
If you have an open loop and water falls and the loops are exposed, all of savings are gone.You may want to think about drilling 4 holes vertical,then bring them into the residents piped to (1-2)systems.