Lítil lygi getur sært vináttu sem hefur verið sterk lengi.

Yes:

• Lítil — small / little, adjective
• lygi — lie, noun
• getur — can, 3rd person singular of geta
• sært — hurt / wound, the form used here after getur
• vináttu — friendship, object form of vinátta
• sem — that / which, introducing a relative clause
• hefur verið — has been
• sterk — strong
• lengi — for a long time / long

So the structure is:

Lítil lygi + getur sært + vináttu + sem hefur verið sterk lengi
= A small lie can hurt a friendship that has been strong for a long time.

Because Icelandic does not have an indefinite article like English a / an.

So:

• lítil lygi can mean a small lie
• vináttu can mean a friendship in context

Icelandic often uses a bare noun where English needs a or an.

Because lygi is a feminine singular noun, and the adjective has to agree with it.

The adjective lítill changes by gender:

• lítill — masculine
• lítil — feminine
• lítið — neuter

Since lygi is feminine, the correct form is lítil.

Also, this is the strong adjective form, which is what you normally use when there is no definite article attached.

Yes. Lygi is the noun a lie, and it is related to the verb að ljúga — to lie.

This is a very common pattern in Icelandic: a noun and its related verb may not look exactly the same in all forms because of older sound changes, but they are clearly connected in meaning.

So:

• að ljúga — to lie
• lygi — a lie

This is a good question because English speakers often expect the dictionary form of the verb.

The dictionary form is að særa — to hurt.
But after verbs like geta, Icelandic normally uses the form sært.

Many grammars call this form the supine. For a learner, the important point is simply:

• að særa — dictionary form
• getur sært — can hurt

So in this sentence, sært is exactly the form Icelandic expects after getur.

Because vináttu is the accusative singular form, and here the word is the direct object of sært.

The basic form is:

• vinátta — friendship

But in this sentence, the friendship is what gets hurt, so Icelandic puts it in the accusative:

• getur sært vináttu — can hurt a friendship

This noun is a weak feminine noun, so the accusative singular ends in -u.

Sem here means that or which and introduces a relative clause.

So:

• vináttu sem hefur verið sterk lengi

means:

• a friendship that has been strong for a long time

A useful thing to know is that sem itself does not change form for gender or case.

It describes vináttu, not lygi.

So the meaning is:

• a friendship that has been strong for a long time

not:

• a lie that has been strong for a long time

The relative clause comes right after vináttu, so it naturally attaches to that noun.

Because sterk is a predicate adjective after hefur verið, and it agrees with the subject of the relative clause.

In the clause:

• sem hefur verið sterk lengi

the understood subject is the friendship. Even though vináttu is accusative in the main clause, inside the relative clause the same thing is the subject of hefur verið.

So the adjective appears as feminine singular nominative:

• sterk

This is one of those places where Icelandic grammar is following the structure of the relative clause, not just copying the case of the earlier noun form.

Hefur verið is the present perfect, just like English has been.

It is made from:

• hefur — has, from að hafa
• verið — been, from að vera

So:

• hefur verið sterk = has been strong

This is a very common Icelandic pattern.

Lengi means for a long time / long.

So:

• hefur verið sterk lengi

means:

• has been strong for a long time

Icelandic often uses lengi without a separate word corresponding to English for in this kind of time expression. That is completely normal.

So the ending of the sentence is very natural Icelandic:

• sterk lengi — strong for a long time