French nouns almost always require an article in French so that would be:

Elle aime le lycée.

This sentence is perfectly idiomatic. Le lycée is likely here the high-school she studies in, work at, or just refer too but might also be high-school in general compared to something else.

Note also that j’écoute la musique means “I listen to the music” so to properly translate “I listen to music”, you would use:

J’écoute de la musique.

Both elle aime lycée and j’écoute musique are always ungrammatical in French, a little like would be “I listen music”.

I

You wouldn’t say in French “Elle aime le lycée.”; it is not idiomatic; what you’d say instead would be something like “Elle aime la vie de lycée.”, or “Elle aime aller à l’école au lycée.”. That is a generic use of “le”.
Here, you are taking “high school” as you do “school” meaning (uncountable, used without the or a) the process of learning in a school, the time during your life when you go to school. You say “She likes high school.” as you say “She likes school.”.

In French you render “She likes school.” by “Elle aime aller à l’école.” or “Elle aime l’école.”; the two possibilities do not exist for “lycée”, though.

Here are clues : ngram1, ngram2

If you are talking about a particular place in which there is such a school besides other things such as a skating ring, a Church and a cinema for instance then you can use “le” according to the second way of using this definite article, that is in a specific mode, and say “Elle aime le lycée.”, but then you do not translate “She likes high school.” but “She likes the high school.”

II

It can be both; if you take “I listen to music.” as meaning “I listen to some music.” you will translate as such:

• “J’écoute de la musique.”.

If you take “music” as the noun “music” used generically, then you say “la musique”;

• J’écoute la musique.

I understand in English, the language learner may ask when to use an article, when to use “the”, etc. When “the” is used, it answers the question “which one?”.

In French, the question is not so much when to use articles, rather when not to use them. As I would be tempted to say always.

However, there are cases where you would not use them. Refer to the use of “article zéro” (Ø) in French to learn more.

Here are examples I found in this thread:

• Pierre qui roule n’amasse pas mousse. (proverbes)
• tambour battant, chemin faisant (archaïsmes, locutions figées)
• Mère décédée. Enterrement demain. (télégrammes)
• Il viendra mardi. (ce mardi-là )
• Maison à vendre. Sucre en poudre. (sur pancartes, étiquettes)
• Venez, jeune homme ! (apostrophe)
• Hommes, femmes, enfants, tout le monde était là. (énumération)
• Le métier de prof. Pierre est avocat. Le lion, roi des animaux. (appositions, attributs)
• Arbre est un nom masculin. (= “Le mot arbre” )
• avoir faim, demander pardon, donner envie, faire fortune, perdre pied,
  prendre feu, rendre service, etc. (locutions verbales).
• avec joie, sans crainte, sur place, etc. (locutions adverbiales)

Some examples: “faire cas” de qqch. Or “j’ai eu vent de …”. “Je vous souhaite bonheur et prospérité”. Etc.

As to the use of articles in English, they do map to something in French.

For example:

• Je mange du fromage** => I eat Ø cheese. (Recall that we don’t say de le, instead it becomes du. If the noun is feminin, use de la)
• Je mange le fromage => I eat the piece of cheese (I don’t think you’d say the cheese (?) )
• Je mange un fromage => I eat a piece of cheese
• J’écoute de la musique => I’m listening to music
• J’écoute la musique => I’m listening to the music (you brought me)

But there are cases where it doesn’t change:

• Le chômage est de 16% et continue de croître. => Unemployment is 16% and keeps rising.

So, just tell yourself that there are always articles. The rare cases where you don’t use them, you’ll learn them as you go. And retain that j’écoute de la musique is I’m listening to music and j’écoute la musique is I’m listening to the music.

edit: By the way, I absolutely don’t see what’s wrong with saying “elle aime le lycée”.