This is where Hungarian struggles. I put "I lie here at the tree and rest" but it wasn't accepted because the computer insists on "lie down" and Hungarian won't, it seems, accept idelefekszik to tell the listener that it is both here and down. There's a bit of guessing involved because we don't know whether the act of lying down is at this moment or whether the speaker is already lying here and resting. With English, the listener is told that it is both down and here so we know that the act of lying down here is all in the present. (I fully expect to be challenged on this!)
Hungarian to English: You need the "down" in English because "I lie here at the tree and rest" sounds like there is no movement. (I think the Hungarian would be "Itt fekszem a fánál, és pihenek") But "lie down" means there is movement.
English to Hungarian: I don't think you can add both le- and ide- I think you could use lefekszik but that tends to be used when going to bed.