Luminous Flux is otherwise known as Lumens. It's a measure of how much light is emitted as a whole. Think of it as how many litres of water comes out of a hose.
Lux is a measure of how much light falls on a given area. Think of it as how much water actually gets on the tree you're watering. If you use a sprinkler, you'll have just as many litres of water (lots of lumens) but not much of it will hit the tree (low lux). If you use a tight nozzle, you have the same amount of water (lots of lumens) and all of it will hit the tree (high lux)
It's all about how focused the beam is.