In "Lucifer Rising" - grammatical explanation for use of -ing form instead of "Rises"?

How does that work grammatically? I guess it's primarily used for titles (movies, songs etc.) but why?

Titles of films are often phrases rather than complete sentences.

In this case, "Lucifer Rising" is an example.

Grammatically, this is a noun phrase, composed of a noun “Lucifer,” and an -ing verb form “Rising.” Traditionally in English, there are two grammatical classifications for the -ing verb form – it’s called a “gerund” when it’s used like a noun, and a “participle” (named the “present participle” or “progressive participle”) when it modifies a noun or is used as part of a verb. In this case, “Rising” is modifying the noun “Lucifer,” so it is considered a participle.

Why "Rising" and not "Rises"?
The use of the progressive participle makes the action seem dynamic and “in progress.” For actions in progress like this, a progressive verb form is preferred over a plain present tense form like "rises."

What's going on with the word order?
Words that modify nouns often come before them in English. So it makes sense to expect the order “Rising Lucifer.” Why is the other order, “Lucifer Rising” also OK, and used so often?

In fact, it is grammatically possible for a participle to come before or after a noun. But it's complicated to explain the choice of position in particular cases.

A participle usually comes after a noun if it has "extra stuff" attached to it. So normal expressions are "a dying man" but "a man dying of leprosy." "A man dying" and "A dying-of-leprosy man" both sound odd, to say the least, to an English speaker.

But, in a title like "Lucifer Rising," there is no extra stuff, just the participle. So, why does it come after?

One explanation might be that it is being treated as a so-called "postpositive adjective" (participles are not exactly adjectives, but they can behave similarly). In languages like French, the normal position for adjectives and participles is after the noun. This has influenced English. In some cases, putting the adjective after the noun has a poetic effect suitable for the title of a work of art. Wikipedia talks about this and has a list of examples in titles:

Titles of books, films, etc. commonly feature nouns with postpositive adjectives. These are often present or past participles (see above), but other types of adjectives sometimes occur.

Examples: Apocalypse Now Redux, Body Electric, Brideshead Revisited, Chronicle of a Death Foretold, A Dream Deferred, Hannibal Rising, Hercules Unchained, The Life Aquatic, A Love Supreme, The Matrix Reloaded, Monsters Unleashed, Orpheus Descending, Paradise Lost, Paradise Regained, Prometheus Unbound, "The Road Not Taken", Sonic Unleashed, Tarzan Triumphant, The World Unseen.

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That's an interesting question. You're right that this pattern is usually used for titles, but it does occur within sentences as well:

I saw John running.

There's a man snorkeling!

Lucifer Rises would be a perfectly good title, but it would have a different feel, because it is a sentence, whereas Lucifer Rising is a noun phrase, not a whole sentence.

I'd like to comment on the "poetic effect" sumelic mentions. Lucifer Rising or London Calling or Bad Moon Rising are all creating ambiguity as you try to parse the title and determine the meaning. Is it a noun phrase, as Colin suggests, and if so, what's the rest of the phrase? Is it "Lucifer is rising," as you might subconsciously attempt to parse the title as a complete sentence? You're going to have to read the book, listen to the song, or watch the movie to find out, right? By only expressing a fragment of a thought, it arouses some curiosity in the reader to complete the thought, or learn what completes the thought.

I'd also note that many of the examples listed in sumalic's list of titles are sequels and the phrasing is probably chosen so that the name of the series appears first. One could argue that "The Matrix Reloaded" is actually "The Matrix: Reloaded" with the colon removed and has nothing to do grammatically with the construction we're discussing. (The X-Men movie series retains an explicit colon in the title--"X-Men: Apocalypse" as an example.)