This reminds me of a method that I read about years ago when the internet was young, but have never tried.
To the best of my recollection, you dig a rectangular pit a little larger than a styrofoam insulation panel of 4'x8' in the ground, can't remember the depth, but am guessing about two feet, maybe less. You line it with heavy plastic (no holes for leakage) fill it with a solution of water and miracle grow type fertilizer. You float the foam panel in the pit and poke holes in it at properly spaced intervals where you insert already started lettuce seedlings - I assume one would need those little baskets you've shown to hold the soil plugs containing the lettuce seedlings.
The theory was that this was maintenence free, only adding water to the solution as it was used by the plants and minimally from evaporation, as the panel covered most of the water. The claim was that you could re-use the same solution for 2 or more lettuce crops. There was no aeration that I can remember, and not sure what they did in case of excessive rainfall (maybe most ran off the raised floating platform?) I think the guy who posted said it was developed by some ag research department in Florida, but at the time I could find no other reference to it. Have always wanted to try it. I've had house plant cuttings and tomato suckers do well in a jar of water with no additives, so it seems worth a shot. Maybe I'll do it half size first?
Dee