These plants can be harvested for decoration purposes without requiring any Power Cells. Lilypads do not "regrow" and will not grow on artificial biomes, they are just part of each newly created gameworld instead and such non-renewable.
If you try to place Lilypads on any kind of liquid, they will not float on the surface of the liquid, but instead displace the unit of liquid just like the lilypad was one full block in size.
To make placed Lilypads float on a liquid, you will have to place any kind of block into the liquid first, then the Lilypad on top of that block and afterwards pick up the block again.
If some more liquid is right next to it, the now empty space where the block has been will automatically be filled with liquid again; otherwise you might have to replace the liquid yourself under the lilypad by placing a unit of liquid there.
Like Reeds and Cattails, Lilypads too cannot be used as Fuel for the Forge, and they are also non-flammable, so they won't burn when Fire Bombs are thrown at them nor when fire spreading is enabled and fire burns right next to them.