Actually Skoo has an idea there. But forget soil, that's not going to work. Anyway the pot would sink with all that weight.
How about DWC? As a first step I propose:
1. Reverse osmosis is used by water companies to stop impurities and let through only pure H2O. This could work in reverse; if a reverse osmosis membrane was used as the "res", then the nutrients would not be able to escape the res but pure water would be able to migrate through from the lake...
2. Some power is obviously needed and this could be a small solar panel floating on a sheet of styrofoam next to the DWC. This would also support a small box of electronics, that would (a) inject a small dose of nutes into the water every so often (b) monitor the pH inside the res and, same as the nutrients, inject either UP or DOWN so as to control the pH automatically at all times. (c) run a little air pump.
The plant would be on top of a styrofoam panel, painted dark of course, and you would want to have weights at the bottom of the res to give stability against wind blowing the whole caboodle over. Or maybe hang the weights off a couple metres of line under, to give even more stability.
I know seeds don't grow through styrofoam so you simply make a hole in the middle and glue in a net pot.
What do you guys think?