Lyfjaskápurinn er læstur.

It is a compound plus the definite article:

• lyfja- = medicine / drugs
• skápur = cabinet, cupboard
• -inn = the

So lyfjaskápurinn is literally the medicine cabinet.

A very common feature of Icelandic is that long words are built out of smaller meaningful parts like this.

In Icelandic compounds, the first part often appears in a special linking form. Here, lyfja- is that compound form, historically related to a genitive plural idea: of medicines.

So although English says medicine cabinet, Icelandic uses lyfjaskápur.

This does not mean you should translate it word-for-word as cabinet of medicines every time. It is just the normal Icelandic compound.

Because Icelandic usually puts the definite article at the end of the noun instead of using a separate word.

So:

• lyfjaskápur = a medicine cabinet
• lyfjaskápurinn = the medicine cabinet

With masculine nouns like skápur, the nominative singular definite form often ends in -urinn:

• skápur → skápurinn
• hestur → hesturinn

That is why you see lyfjaskápurinn rather than a separate word for the.

Er is the present tense, 3rd person singular form of vera, which means to be.

So:

• ég er = I am
• þú ert = you are
• hann / hún / það er = he / she / it is

In this sentence, er simply means is.

It is in the nominative singular.

Why?

• It is the subject of the sentence.
• The subject of a basic sentence like this is normally nominative in Icelandic.

It is also masculine singular, which matters because læstur has to agree with it.

Because læstur agrees with lyfjaskápurinn, which is masculine singular nominative.

The forms are:

• masculine: læstur
• feminine: læst
• neuter: læst

So you get:

• Lyfjaskápurinn er læstur. = masculine
• Hurðin er læst. = feminine, because hurð is feminine
• Herbergið er læst. = neuter, because herbergi is neuter

This kind of agreement is very important in Icelandic.

It is originally the past participle of læsa, meaning to lock, but in a sentence like this it behaves very much like an adjective.

So in practice, you can think of it as describing the state of the cabinet:

• læstur = locked

That is why it changes form to match gender, number, and case, just like an adjective does.

Yes. This is a very normal Icelandic statement pattern:

• subject
  • verb
    • description/complement

So:

• Lyfjaskápurinn = subject
• er = verb
• læstur = complement

In this sentence, the word order is very close to English.

Move the verb to the front:

• Er lyfjaskápurinn læstur? = Is the medicine cabinet locked?

That verb-first pattern is the normal way to make a yes/no question in Icelandic.

Add ekki after the finite verb:

• Lyfjaskápurinn er ekki læstur. = The medicine cabinet is not locked.

That placement is very common in simple Icelandic sentences:

• Hann er ekki heima.
• Bíllinn er ekki nýr.

This is a very useful distinction:

• læstur = locked
• lokaður = closed

So a cabinet can be:

• lokaður but not læstur = closed but not locked
• lokaður og læstur = closed and locked

English learners often mix these up because English sometimes uses closed in situations where Icelandic would clearly prefer locked.

A rough English-friendly approximation is:

LIV-ya-skow-pu-rin er LYE-stur

A few helpful pronunciation points:

• y sounds basically like i in modern Icelandic
• f between vowels is often pronounced like v, so lyfja sounds like liv-ya
• á sounds roughly like ow in now
• æ sounds roughly like eye
• Icelandic r is usually tapped or trilled, not an English-style r

Also, Icelandic normally stresses the first syllable of the word, so:

• LYFjaskápurinn
• LÆStur