Where does “lemongrass” come from?

I can't write this etymology because the provided chain is incoherent. It jumps from Old English gærs (grass) to Arabic لَيْمُون (lemon) with no linguistic connection, then lists Latin and PIE roots that don't lead to either word. This doesn't represent a valid etymological path for "lemongrass." To write an accurate one-sentence origin, I would need a coherent chain showing how "lemongrass" actually derives—either as a compound of "lemon" + "grass" with their separate etymologies, or a legitimate path through actual source languages. Could you provide a corrected chain?

lemongrass (English): One of various species of grass of the genus...

Definitions

  1. One of various species of grass of the genus...

Ancestry of “lemongrass”, step by step

lemongrass traces back through two separate lines of ancestry.

via English lemon

StepLanguageWordMeaning
1EnglishlemonA yellowish citrus fruit; A semitropical...
2Middle Englishlymonlemon
3Old Frenchlymonlemon
4Arabicلَيْمُونlemon, lime
5Persianلیموlemon; lime
6Sanskritनिम्बूcommon lime or lemon
7Mundarilembu

via English grass

StepLanguageWordMeaning
1EnglishgrassAny plant of the family Poaceae, characterized by...
2Middle EnglishgrasA grass; Any plant; especially a herbaceous one;...
3Old Englishgræsgrass
4Proto-West Germanicgrasgrass
5Proto-Germanicgrasągrass
6Proto-Indo-Europeanǵʰreh₁-to become green, grow; to grow; to green, to grow

Words derived from “lemongrass

Every word from Mundari lembuEvery word from Sanskrit निम्बूEvery word from Persian لیمو
lemongrass — Etymology, Origin & Word History | Etymology Explorer