Lánþeginn ber ábyrgð á meðferð safnefnisins.

It is a fixed expression meaning is responsible for.

Literally, bera ábyrgð á means to bear responsibility for:

• bera = to carry, bear
• ábyrgð = responsibility
• á = for / over / concerning, depending on context

So even though the literal image is bearing responsibility, in natural English you usually translate it as be responsible for.

Bera is the infinitive, meaning to bear / carry.
Ber is the 3rd person singular present tense form:

• ég ber = I bear / carry
• þú berð = you bear / carry
• hann/hún/það ber = he/she/it bears / carries

Since the subject is Lánþeginn (the borrower), Icelandic uses ber.

The -inn is the suffixed definite article, meaning the.

So:

• lánþegi = borrower
• lánþeginn = the borrower

Icelandic usually attaches the to the end of the noun instead of putting it as a separate word in front.

It is nominative singular, because it is the subject of the sentence.

The subject is the person or thing doing the action:

• Lánþeginn = the borrower
• ber = bears / is responsible
• ábyrgð = responsibility

So lánþeginn is in the case normally used for subjects: nominative.

It is the direct object of ber, so it is in the accusative.

However, the form ábyrgð looks the same as the nominative. That is normal for many Icelandic nouns: the case is determined by grammar, not always by a visible ending change.

So in this sentence:

• Lánþeginn = subject
• ber ábyrgð = literally bears responsibility

Here á belongs to the expression ábyrgð á einhverju, which means responsibility for something.

In this usage, á takes the dative.

So meðferð is functioning as dative singular here. The tricky part is that the noun meðferð has the same form in several cases, so you do not see an obvious ending change.

In other words:

• ábyrgð á meðferð ... = responsibility for the handling / treatment ...

Because it is genitive singular definite, and it depends on meðferð.

The phrase is:

• meðferð safnefnisins = the handling of the collection item/material

English often uses of for this relationship, but Icelandic very often uses the genitive case instead.

Breakdown:

• safnefni = collection item / collection material
• safnefnis = of a collection item
• safnefnisins = of the collection item

The ending -ins is the definite genitive singular ending for this neuter noun.

Because Icelandic often expresses of relationships through the genitive case rather than a separate preposition.

So instead of something like handling of the collection item, Icelandic uses:

• meðferð safnefnisins

This is very common in Icelandic:

• noun + genitive noun
  to express possession, relation, or of-type meanings.

Safnefni is a somewhat formal/institutional word. It usually refers to an item in a collection or collection material, especially in contexts like libraries, archives, or museums.

Depending on context, it might be translated as:

• collection item
• library material
• archival material
• museum object

So the exact English wording can vary a bit depending on what kind of institution the sentence comes from.

Yes. It has a very normal subject–verb–object/complement structure:

• Lánþeginn = subject
• ber = verb
• ábyrgð = object
• á meðferð safnefnisins = prepositional phrase explaining what the responsibility concerns

So this is a straightforward, neutral sentence structure, especially in formal or legal-style language.

Yes. The sentence sounds formal and would fit well in rules, regulations, library policies, contracts, or official notices.

A big reason is the expression bera ábyrgð á, which is common in formal Icelandic.
Also, words like meðferð and safnefni are more formal than everyday conversational vocabulary.

These are two Icelandic letters that English speakers usually notice right away:

• þ is like the th in thing
• ð is like the th in this

So in this sentence:

• lánþeginn has þ = like th in thing
• ábyrgð ends with ð, which is related to the voiced th sound, though final pronunciation can be softer or less fully voiced depending on speech

You do not need to pronounce them exactly like English th in every environment, but that comparison is the best starting point.