"the lemons" (those we're seeing, those we're talking about, etc.) = "les citrons" anyway and always
1) either "des citrons" if it is undetermined (e.g. I brought lemons -- J'ai apporté des citrons ; They sell lemons -- Ils vendent des citrons ; You make this cake with lemons -- Tu fais ce cake avec des citrons), or when there is no context, as in exercises on Duolingo.
2) or "les citrons", if the meaning is general (attention: general does not equal undetermined, but "all of..."). E.g.: "Lemons are sour / good for health / yellow" -- "LES citrons sont acides / bons pour la santé / jaunes".
Beware, "des" does not always imply undetermined objects, because in French "des" is also the contraction of "de + les"; subsequently, this falls in the first category mentioned above. It happens when the word (generally a verb) before is constructed with "de". E.g.: "avoir besoin DE" (to need), "s'occuper DE" (to be in charge of, to deal with), "avoir envie DE" (to fancy, to feel like). Imagine you're making a cake with a friend, several ingredients in front of you, and you say "OK, now I need the lemons" -- "OK, maintenant j'ai besoin DES citrons" (literally "de les citrons", which is a mistake in French, not even colloquial or slang, really a total mistake that hurts the ears).
The same case with undetermined objects is made using simply the phrasal "de", dropping the "les". E.g. "I need lemons for my cake" -- "J'ai besoin DE citrons pour mon cake". yes, it's weird and complicated at first, but you get used to it with practice...
"They've the lemons." is the weirdest possible correction. Not impossible, but really weird and obscure!
I'm not an expert, but I have figured out that Duo usually wants you to leave out the article in English if it sounds unnatural or unnecessary.
You almost always need an article in front of a noun in French so you should put in whichever article makes sense for the sentence. The only times (I know of) where you don't need an article in French are
in front of an occupation (I guess the French think of occupations as adjectives?),
after the word pas (just use de without le/la), and
between the verb parler and the name of a language.
Can anyone else think of more?