I"Il aime les citrons" usually means "He likes lemons" (in general), but it can also mean "He likes the lemons" (if we are talking of lemons in particular).

("Il aime des citrons" could be translated as: "He likes some lemons", i.e. not all of them.)

"They eat sandwiches" (in general), and "They eat some sandwiches" (a number of them) are both translated into "Ils mangent des sanwhichs" in French.

"They eat some sandwiches" can also be translated into "Ils mangent quelques sanwhichs" (= a few) and "Ils mangent certains sanwhichs" (a certain type).

I'm learning french as well but as far as I got it, "Il aime les citrons" is definite, i.e., you know which lemons you are talking about. E.g., he likes the lemons he just bought. The use of "the" depends on the context, I guess.

"Il aime des citrons" is about lemons in general. E.g., he likes lemons for dessert. The use of "some" also depends on context as it is implied in the "des" in french. It can be explicit for some like to address types: "Il aime quelques citrons verts." / He likes some (types of) limes.

I don't know why you use examples with different persons and nouns. To me, as I understood this, it doesn't matter if it is "il" or "ils", "citrons" or "sandwichs".

"il aime des citrons" does not make much sense anyway. if you want to give a general information about his likes and dislikes, you would say "il aime le citron" unlike "il aime les fraises" because you hardly ever eat more than one lemon at a time.

Ok, so I was wrong about this, sorry for the confusion. And thanks for the feedback. But now this raises two questions to me: 1) I cannot use "Ils mangent les sandwhichs."? 2) should I use "des" only when referring to "some"?

yes, please use "des" when you refer to "some" (meaning: a number of), and use "les" whenever you are referring to precise objects, like "Ils mangent les sandwiches (que j'ai préparés/ qu'ils ont commandés...)".