Translation:The athlete does not run in onto the grass, but sits down onto the ground.
A field of grass is usually a very flat thing, so fűre alone would cover that, or you could use ráfut - "to run onto" instead of befut. Unless the grass here is particularly high, I would say that it is enclosed somehow, maybe by a fence.
Considering the entire sentence, I'd say that our sportsperson isn't to keen to run onto the field (which is in the centre of the stadium, so they'd have to "run in"), but stays on the outskirts and sits down there.
My issue is the lack of consistency with how "sits down onto" is translated.
In previous sentences, if there were words with an "re" suffix in the sentence it made you omit the "le" in "leül." In those examples, some users pointed out that, "if you are sitting onto something it is assumed you are sitting down onto something so you don't need the prefix 'le'."
But in this sentence, "le" is mandatory...why now and not before?
Short answer: it isn't needed.
Slightly longer answer: but it sounds better, since the (negated) verb in the first clause has a prefix as well.
Long answer: English is awful. With a simple "sit" it's hard to tell if there's a movement going on or not, so "sit down" is often choosen to indicate such a movement, even if you're not actually moving downwards. A thing like that is not needed in Hungarian, since the type of suffix already indicates if there's a movement going on: mostly -n for static sitting, and -ra/-re for a movement.
In accordance with that, ül can refer to both static sitting and a movement, depending on the noun suffix. On the other hand, ül with almost any prefix can only be a movement: leül, felül, elül, ideül, átül - it's mostly translated as "sitting down" in some fashion.
But one more thing to consider with that is the perfective meaning the verbal prefixes give you: a verbal prefix not only changes the meaning of the verb, but can also indicate that this is a one-time occurrence instead of a regular thing.