Naš stan je na drugom katu, ali lift ne radi.

Because na drugom katu answers the question where? — on the second floor.
After na, Croatian uses the locative case when talking about location.

• na drugom katu = on the second floor (location)
• na drugi kat = onto the second floor (movement/direction)

So:

• Stan je na drugom katu. = The apartment is on the second floor.
• Idem na drugi kat. = I’m going to the second floor.

Drugom katu is in the locative singular.

Both words change because:

• drugom is the adjective/ordinal second
• katu is the noun floor

In Croatian, adjectives must agree with the noun in:

• gender
• number
• case

Since kat is masculine singular and here it is in the locative, the whole phrase becomes:

• drugi kat → nominative
• na drugom katu → locative

Yes. Naš means our.

It is a possessive adjective, and it agrees with the noun it describes.

Because stan is masculine singular, the form is:

• naš stan = our apartment

Other forms would change depending on the noun:

• naša kuća = our house
• naše dijete = our child
• naši prijatelji = our friends

Stan usually means apartment or flat — a place to live in a larger building.

It is one of the most common words for apartment in Croatian.

Related words:

• kuća = house
• zgrada = building
• soba = room

So Naš stan means our apartment/flat.

Je is the 3rd person singular form of the verb biti (to be).

So:

• stan je = the apartment is

Unlike in some languages where the verb to be can be omitted, in Croatian it is normally expressed in this kind of sentence.

So:

• Naš stan je na drugom katu. = Our apartment is on the second floor.

In Croatian, raditi is very commonly used for machines, devices, and systems to mean:

• to work
• to function
• to be operating

So:

• Lift radi. = The elevator works / is working.
• Lift ne radi. = The elevator doesn’t work / isn’t working.

This is a very natural Croatian way to say something is out of order.

Yes. Both exist.

• lift = elevator/lift
• dizalo = elevator

In everyday speech, lift is very common, especially in urban settings.
Dizalo is also correct and may sound a bit more standard or formal in some contexts.

So both are possible:

• Lift ne radi.
• Dizalo ne radi.

Yes. Ali means but.

It connects two contrasting ideas:

• Our apartment is on the second floor
• but the elevator isn’t working

So it works just like English but in this sentence.

Croatian does not have articles like English a/an/the.

The noun stan can mean:

• an apartment
• the apartment

Which one is meant depends on context.

Here, because of naš (our), the meaning is naturally definite:

• naš stan = our apartment

So Croatian does not need a separate word for the.

Not always. Kat is a common word for a floor/story of a building, especially in Croatian usage.

You may also encounter:

• prizemlje = ground floor
• prvi kat = first floor
• drugi kat = second floor

In some varieties of the wider region, you may also hear sprat, but in standard Croatian kat is the usual word.

Linguistically, drugi kat does mean second floor.

But learners should be careful because floor numbering conventions can differ by country. In Croatian:

• prizemlje = ground floor
• prvi kat = first floor
• drugi kat = second floor

So in this sentence, na drugom katu is literally and normally on the second floor.

The basic structure is:

• Naš stan = subject
• je = verb
• na drugom katu = location
• ali = but
• lift = subject
• ne radi = verb phrase

Croatian word order is more flexible than English, so some variation is possible for emphasis. But this version is very natural and neutral:

• Naš stan je na drugom katu, ali lift ne radi.

For a learner, this is a good standard pattern to remember.

Croatian usually forms negation by putting ne before the verb.

Examples:

• Radi. = It works.

• Ne radi. = It doesn’t work.

• Je ovdje. = It is here.
• Nije ovdje. = It isn’t here.

Notice that with je, the negative form is usually written together as nije.
But with radi, it stays separate:

• ne radi

So in your sentence:

• lift ne radi = the elevator doesn’t work

Yes, very easily. It is a useful pattern:

• Naš stan je na + locative, ali + something + ne radi.

Examples:

• Naš ured je na trećem katu, ali lift ne radi.
  Our office is on the third floor, but the elevator doesn’t work.

• Moja soba je na prvom katu.
  My room is on the first floor.

• Restoran je u prizemlju.
  The restaurant is on the ground floor.

This sentence is especially useful because it combines:

• possession (naš)
• location (na drugom katu)
• contrast (ali)
• negation (ne radi)