Ég lét laga saumavélina í gær, því hún stoppaði alltaf.

This is a very common Icelandic pattern: láta + infinitive can mean to have something done.

So:

• Ég lét laga saumavélina = I had the sewing machine repaired
• literally, it looks like I let repair the sewing machine, but in normal usage it is a causative construction

A few similar examples:

• Ég lét þrífa bílinn. = I had the car cleaned.
• Hún lét klippa hárið. = She had her hair cut.

So in this sentence, lét does not mean that the speaker gave permission. It means they arranged for someone to repair the machine.

Lét is the past tense of láta.

Basic forms:

• að láta = to let, allow, have something done
• ég læt = I let / I have done
• ég lét = I let / I had done

In this sentence, it is past tense because the whole event happened yesterday:

• Ég lét laga saumavélina í gær = I had the sewing machine repaired yesterday.

Because saumavélina is the accusative singular definite form.

The word is:

• saumavél = sewing machine
• saumavélin = the sewing machine (nominative)
• saumavélina = the sewing machine (accusative)

Here it is the direct object of laga (repair/fix), so Icelandic uses the accusative.

Compare:

• Saumavélin stoppaði. = The sewing machine stopped.
  
  • subject, so nominative
• Ég lét laga saumavélina. = I had the sewing machine repaired.
  
  • object, so accusative

Because saumavél is a feminine noun in Icelandic.

That means when you refer back to it with a pronoun, you use:

• hún = she / it (for feminine nouns)

So:

• saumavélin = the sewing machine
• hún stoppaði alltaf = it always stopped

English uses it for things, but Icelandic often uses a gendered pronoun that matches the noun’s grammatical gender.

Here því means because.

In Icelandic, there are a few ways to express because, including:

• því
• af því að

In this sentence, því is a shorter and very natural way to introduce the reason:

• Ég lét laga saumavélina í gær, því hún stoppaði alltaf.
• I had the sewing machine repaired yesterday, because it always stopped.

So því is not the dative form of það here in the usual sense you might first think of; it is functioning as a conjunction meaning because.

Because the sentence is talking about a repeated problem in the past.

• alltaf = always
• stoppaði = stopped

So hún stoppaði alltaf means:

• it always stopped
• in other words, whenever the speaker used it in that period, it kept stopping

This is very natural in both Icelandic and English: always does not have to refer to the present; it can describe repeated past behavior too.

Stoppaði is the past tense of stoppa.

• að stoppa = to stop
• hún stoppar = it stops
• hún stoppaði = it stopped

This is a weak verb, and the -ði ending is a common past-tense marker in Icelandic.

So:

• hún stoppaði alltaf = it always stopped

That is the normal word order here.

In a main clause like this, Icelandic often places the finite verb early, and adverbs such as alltaf often come after it:

• hún stoppaði alltaf

This is very natural Icelandic word order. English can also do something similar:

• it always stopped

But Icelandic and English do not always place adverbs in exactly the same spot, so it is best to learn common patterns from examples.

Yes. Semantically, repairing is the action that happened to the sewing machine, but grammatically the finite verb is lét.

Structure:

• Ég = subject
• lét = finite verb in past tense
• laga = infinitive
• saumavélina = object of laga

This is typical of the causative construction:

• Ég lét laga ... = I had ... repaired

So laga stays in the infinitive because it depends on lét.

Normally, no. It strongly suggests that someone else repaired it, and the speaker arranged for that to happen.

• Ég lét laga saumavélina = I had the sewing machine repaired

If you want to say I repaired it myself, you would usually say:

• Ég lagaði saumavélina. = I repaired the sewing machine.

So the difference is important:

• Ég lagaði ... = I did the repair
• Ég lét laga ... = I had it repaired / someone repaired it for me

Because the sentence has two clauses:

1. Ég lét laga saumavélina í gær
2. því hún stoppaði alltaf

The second clause gives the reason for the first one, so a comma is very natural here. Icelandic punctuation often uses commas in places that may feel a bit more frequent or structured than in informal English writing.

So the comma helps separate:

• the main statement
• the explanation/reason

Í gær is the standard expression for yesterday.

It is simply a fixed time expression you should learn as a chunk:

• í dag = today
• í gær = yesterday
• á morgun = tomorrow

Even though í often means in, in expressions like í gær you should think of the whole phrase as one unit meaning yesterday.

Laga normally takes a direct object in the accusative when you are fixing something.

So:

• að laga saumavélina = to repair the sewing machine

That is why the noun appears as saumavélina, not nominative saumavélin.

This is worth learning with the verb:

• laga eitthvað = fix something

Yes, it could, although the sentence would then be structured a little differently in normal Icelandic word order.

For example:

• Því hún stoppaði alltaf lét ég laga saumavélina í gær.

That is grammatical, but it sounds more marked or literary. The original sentence is much more natural in everyday speech:

• Ég lét laga saumavélina í gær, því hún stoppaði alltaf.

So for learners, the original order is the best pattern to copy.