Bagaj dolabı kilitli.

• bagaj = baggage, luggage
• dolabı = cabinet, locker, cupboard
• kilitli = locked, lockable, with a lock

So bagaj dolabı is a set phrase meaning baggage locker or luggage locker, and kilitli describes it.

In Turkish, sentences in the present tense often do not need an explicit verb meaning to be.

So:

• Bagaj dolabı kilitli = The luggage locker is locked

This is completely normal Turkish.
English needs is, but Turkish often leaves it out in simple present statements like this.

Kilitli is an adjective.

It comes from:

• kilit = lock
• -li / -lı / -lu / -lü = a suffix meaning with, having, or sometimes forming adjectives

So kilitli literally suggests with a lock, and in many contexts it means locked.

In this sentence, it functions as a predicate adjective: it tells you the condition of the locker.

Here, -ı is not the accusative ending.

Bagaj dolabı is a Turkish noun compound. In these compounds, the second noun usually takes a special ending that looks like the third-person possessive suffix.

So:

• bagaj dolabı = baggage locker
• not bagaj dolap

This is a very common Turkish pattern:

• otobüs durağı = bus stop
• yatak odası = bedroom
• kahve fincanı = coffee cup

So in this sentence, dolabı is just part of the compound noun bagaj dolabı.

It is basically one noun phrase, a compound meaning luggage locker.

Even though it is written as two words, Turkish treats it as a compound structure:

• bagaj tells you what kind of locker it is
• dolabı is the main noun

So it works like English phrases such as coffee cup or office door, except Turkish uses a different grammatical structure.

Turkish often puts the thing being talked about first, and then gives information about it.

So:

• Bagaj dolabı = the luggage locker
• kilitli = locked

This order is very natural because Turkish commonly places the subject/topic first and the description after it.

If you said Kilitli bagaj dolabı, that would usually mean the locked luggage locker as a noun phrase, not a complete sentence.

So:

• Bagaj dolabı kilitli = The luggage locker is locked.
• Kilitli bagaj dolabı = the locked luggage locker

Yes.

• Bagaj dolabı kilitli = normal, everyday style
• Bagaj dolabı kilitlidir = also correct, slightly more formal or definite

The ending -dir / -dır / -dur / -dür can add a more formal, factual, or emphatic tone.

In normal conversation, people very often just say kilitli without -dir.

You use değil.

• Bagaj dolabı kilitli değil. = The luggage locker is not locked.

This is the usual way to negate this kind of adjective-based sentence in Turkish.

Use the question particle mi.

• Bagaj dolabı kilitli mi? = Is the luggage locker locked?

The particle changes form depending on vowel harmony, but here it is mi.

It can vary by context.

Depending on the situation, kilitli can mean:

• locked
• lockable
• having a lock

In Bagaj dolabı kilitli, the most natural meaning is usually the luggage locker is locked.

Context decides the exact nuance.

Not always.

Bagaj can refer to:

• luggage or baggage in travel contexts
• the trunk/boot of a car in some contexts

But in bagaj dolabı, it clearly means something like baggage / luggage, so the phrase means luggage locker.

A rough pronunciation guide is:

bah-GAHJ doh-LAH-buh kee-LEET-lee

A few notes:

• gaj in bagaj sounds a bit like the end of garage
• ı in dolabı is the Turkish undotted ı, a sound English does not have exactly; it is not a clear ee
• stress is commonly heard around dolabı on -la-, and in kilitli on -lit-

Yes.

• Bu bagaj dolabı kilitli. = This luggage locker is locked.

That is completely natural.
You can also say:

• Şu bagaj dolabı kilitli. = That luggage locker is locked.
• O bagaj dolabı kilitli. = That luggage locker is locked.

These words help specify which locker you mean.

Usually not, unless you specifically want the sense of a / one.

• Bagaj dolabı kilitli. = The luggage locker is locked. / A luggage locker is locked.
  The exact English article depends on context.
• Bir bagaj dolabı kilitli. = One luggage locker is locked / A certain luggage locker is locked

Turkish does not use articles the same way English does, so leaving out bir is very normal.