Hún varð hissa, en hún viðurkenndi að þetta hefði verið lygi.

Because verða means to become / to get, while vera means to be.

So:

• hún varð hissa = she became surprised / she got surprised
• hún var hissa = she was surprised

The sentence is talking about a change of state, so varð is the natural choice.

Hissa means surprised.

In modern Icelandic, it is very commonly used in expressions like:

• vera hissa = to be surprised
• verða hissa = to become/get surprised

For a learner, the safest thing is to remember it as part of these common combinations. In this kind of use, it normally just appears as hissa.

Because en joins two separate clauses, and Icelandic normally states the subject in each clause.

So the sentence is built like this:

• Hún varð hissa
• en hún viðurkenndi að þetta hefði verið lygi

English can sometimes sound natural with less repetition, but Icelandic usually keeps the subject explicit here.

En means but.

It is a coordinating conjunction, linking two main clauses of equal status:

• She became surprised
• but she admitted...

So there is nothing especially tricky about en itself; it simply contrasts the two parts of the sentence.

Viðurkenndi is the 3rd person singular past of viðurkenna, which means to admit or to acknowledge.

So:

• ég viðurkenni = I admit
• hún viðurkenndi = she admitted

The ending -di is a normal past-tense ending for many weak verbs.

Because Icelandic commonly uses að to introduce a content clause, very much like English that.

So:

• hún viðurkenndi að ... = she admitted that ...

In English, that is often omitted, but in Icelandic að is very common in this structure.

Hefði verið is a perfect construction built from:

• hefði = past subjunctive of hafa
• verið = the form of vera used in perfect constructions

Together, hefði verið means something like:

• had been
• sometimes, depending on context, simply was

So þetta hefði verið lygi means that the thing being referred to is being presented as having been a lie.

Because Icelandic often uses the subjunctive in subordinate clauses that report what someone said, thought, admitted, believed, and so on.

Here, the clause after viðurkenndi að is not just a plain factual statement from the narrator's point of view. It is presented as the content of her admission. That is why hefði verið is very natural.

Very roughly:

• hafði verið = more straightforward, factual had been
• hefði verið = reported/admitted content, often with a bit more distance from the narrator

This is a very common Icelandic pattern and one that English speakers often need time to get used to.

Not really, even though hefði can sometimes correspond to English would have.

In this sentence, hefði verið is best understood as part of a subjunctive reported clause, not as a conditional meaning would have been.

So here it is better understood as:

• had been
• or sometimes was, depending on how naturally you want to translate it into English

That is a common point of confusion for learners.

Þetta means this, and here it refers to the matter, statement, or thing under discussion.

A useful point is that Icelandic often uses neuter singular when referring to a whole situation, idea, or statement. So þetta does not have to match the gender of lygi.

In other words:

• þetta = this matter / this thing / this
• lygi = a lie

The pronoun points to the situation; the noun names what that situation was.

Lygi is nominative singular of the feminine noun lygi, meaning lie.

There is no article because it means a lie, not the lie.

So:

• lygi = a lie
• lygin = the lie

After vera and similar constructions, predicate nouns are typically in the nominative, so lygi is exactly what you would expect here.

Because this is a normal Icelandic subordinate clause.

The order is:

• að = introducing the clause
• þetta = subject
• hefði = finite verb
• verið = non-finite verb form
• lygi = predicate noun

So the structure is quite regular. Unlike German, Icelandic does not push the verb all the way to the end in this kind of clause.

Either may be right depending on context and how natural you want the English to sound.

A more form-based translation is:

• this had been a lie

But in smoother English, especially in narration, you might also say:

• this was a lie

The Icelandic form is doing grammatical work that does not always map neatly onto one single English tense choice, so both are possible depending on context.