Translation:The giraffe lies down here and the zebras hurry away.
I imagine that all versions of "preverb implying motion" + fekszik will translate as "lie down" in English, not just lefekszik (lie + down) but also e.g. idefekszik (lie + to here) -- the latter would imply that he moves here and at the end of the movement is in a lying position.
Yes, but no. :)
"To lie" is usually regarded as static ("I've been lying here for a while") while "to lie down" is a movement. But that movement doesn't have to be downwards. You can also "lie down" in the upper part of a bunkbed.
"Lefekszik ide" would be a literal translation, but it's overspecifying things. So much that you'd wonder where "down" is. Idefekszik is much better to capture that "get here, lie down" meaning.
Tl;dr: English is terrible.