The man was lying down on the floor.
The man was lying on the floor.
What's the difference between the two sentences?
In many contexts, adding preposition down after lying is purely a stylistic choice with no effect on meaning. But sometimes lying down implies a "volitional" action by a conscious agent, so...
1: The man was lying down on the floor (perfectly natural)
2: The body was lying down on the floor (unlikely)
3: The litter was lying down on the floor (very unlikely)
...where all three of the above would be fine without down.