A lake has very deep water at the bottom, in the benthic zone. why is it more difficult for plants to live in the benthic zone of this lake than in the littoral zone?

This is because benthic zone are too dark to support photosynthesis. Due to their depths, sunlight is unable to penetrate the above lying waters and reach the region. This way plants cannot carry out photosynthesis hence cannot grow. This is why only decomposers, detritus feeders can be found in the benthic zone.