I did not have luck with Duckweed (I KNOW!!!! ), Red root floaters or Salvinia Minima but the Dwarf water lettuce is growing great for me. Hood lids not glass. Could be my stinkin hard water though.Unless you are keeping fish that like to jump (like hatchet fish), it may not be necessary to have a lid. There are advantages and disadvantages to a lid. I try not to use a lid unless I have to do so. I once kept a saltwater tank with a snowflake eel who could slither right out of the tank if I left any opening greater than 1/2 inch.
I have water sprite (aka Asian Water Fern) in my tanks. They are stem plants that can grow rooted or left floating. In one of my tanks, the stems grow about 4 inches above the top of the tank and I have to prune them occasionally. If I had a lid on the tank, they would bump against the lid.
Floating plants generally like a lot of light. One reason they grow at the water surface is that they have access to direct sunlight.