Jeg har lyst til at blive hjemme i aften, men min veninde har lyst til at gå en tur ved havet.

In Danish, lyst is a noun, not an adjective in this expression. The full pattern is:

at have lyst til + something / at-infinitive

So:

• Jeg har lyst til kaffe. = I feel like coffee.
• Jeg har lyst til at blive hjemme. = I feel like staying home.

A literal breakdown is something like I have desire to..., but in natural English it usually means I feel like... or I want to....

Because lyst normally takes til.

The structure is:

have lyst til + noun
or
have lyst til + at + verb

Examples:

• Jeg har lyst til pizza.
• Jeg har lyst til at sove.

So in your sentence:

• har lyst til at blive hjemme
• har lyst til at gå en tur

The til belongs with lyst, and the at introduces the infinitive verb.

Because they do different jobs.

• til is the preposition required by lyst
• at marks the infinitive verb

So:

• lyst til = desire for / feel like
• at blive = to stay
• at gå = to walk

English often hides this structure more than Danish does, so it can feel a bit repetitive at first, but it is completely normal.

Yes, blive often means become, but it can also mean remain or stay, depending on context.

Here:

• blive hjemme = stay home / stay at home

Other examples:

• Jeg bliver hjemme i dag. = I’m staying home today.
• Han blev længe. = He stayed a long time.

So blive is a flexible verb, and context tells you whether it means become or stay.

This is a very common learner question.

In Danish:

• hjem usually expresses movement/direction: home
• hjemme usually expresses location: at home

Compare:

• Jeg går hjem. = I’m going home.
  (movement toward home)
• Jeg er hjemme. = I’m at home.
  (location)

In your sentence, blive hjemme means stay at home, so the location form hjemme is needed.

I aften means this evening / tonight.

Danish often uses i in time expressions:

• i dag = today
• i morgen = tomorrow
• i aften = tonight / this evening

So you should learn i aften as a fixed time expression.

A useful contrast:

• i aften = this evening / tonight
• i nat = tonight, during the night

So if you mean the evening, i aften is correct.

Veninde means female friend.
Ven usually means male friend or just friend in some contexts, but veninde clearly marks that the friend is female.

So:

• min ven = my friend (often male)
• min veninde = my female friend

A native English speaker may notice that Danish often marks gender in words like this where English usually does not.

Because men is a coordinating conjunction, like but in English. It joins two main clauses.

Your sentence has:

1. Jeg har lyst til at blive hjemme i aften
2. men min veninde har lyst til at gå en tur ved havet

After men, Danish keeps normal main-clause word order, meaning the finite verb stays in second position.

So:

• men min veninde har lyst ...

This is different from many subordinate conjunctions, which change the sentence structure.

Yes, but the nuance is a little different.

• Jeg har lyst til at blive hjemme = I feel like staying home
• Jeg vil gerne blive hjemme = I would like to stay home

Har lyst til often sounds more like a personal inclination or mood.
Vil gerne often sounds more like a wish or preference.

In many situations, both work, but har lyst til is especially good for talking about what you feel like doing.

Gå en tur is a very common Danish expression meaning:

• go for a walk
• take a walk

Literally, it is walk a trip/round, but idiomatically it means take a walk.

Compare:

• gå = walk
• gå en tur = go for a walk

So in your sentence:

• at gå en tur ved havet = to go for a walk by the sea

This is much more natural than just gå, if you mean taking a walk for pleasure.

Because tur is a common gender noun in Danish, so it takes en.

• en tur
• turen
• flere ture

This is simply something you have to learn with the noun.

Ved often means by, near, or beside.

So:

• ved havet = by the sea / near the sea

It tells you the location of the walk.

Compare:

• ved havet = by the sea
• til havet = to the sea
• i havet = in the sea

So ved is the natural choice when someone is walking alongside or near the sea.

Because havet is the definite form: the sea.

In Danish, definiteness is often added as an ending:

• et hav = a sea
• havet = the sea

So ved havet literally means by the sea.

This is one of the biggest differences from English: Danish often puts the onto the end of the noun instead of using a separate word.

Yes, depending on context, ved havet can be translated as:

• by the sea
• near the sea
• at the seaside

The exact English wording depends on what sounds most natural in the situation, but the Danish phrase itself is straightforward: it places the action close to the sea.

Because each clause has its own infinitive verb phrase:

• har lyst til at blive hjemme
• har lyst til at gå en tur ved havet

Each har lyst til needs its own at + verb afterwards. Danish does not normally skip the second at here.

It sounds very natural and conversational. The structure suggests a contrast in preferences:

• I feel like staying home tonight
• but my friend feels like taking a walk by the sea

So it gives the sense that the two people want different things. The conjunction men makes that contrast clear.

Yes. The finite verb in both clauses is har, which is the present tense of have.

• Jeg har lyst ...
• min veninde har lyst ...

Even though the sentence refers to something happening i aften, the grammar is still present tense, just like English often uses present forms for current wishes about later plans.

A useful breakdown is:

• Jeg = subject
• har = finite verb
• lyst til = fixed expression
• at blive hjemme = infinitive phrase
• i aften = time expression
• men = coordinating conjunction
• min veninde = subject
• har = finite verb
• lyst til = fixed expression
• at gå en tur = infinitive phrase
• ved havet = place expression

Seeing the sentence in chunks like this makes it much easier to understand and reuse in your own Danish.