Il deterioramento e lo smarrimento richiedono una nuova emissione.

Because Italian has more than one form of the masculine singular definite article.

• il is the normal form before most consonants: il deterioramento
• lo is used before certain sounds, including s + consonant: lo smarrimento

Since smarrimento begins with sm-, it takes lo, not il.

A few similar examples:

• il libro
• lo studente
• lo sbaglio
• lo zaino

Because the subject is made of two nouns joined by e.

So:

• Il deterioramento richiede... = singular subject
• Lo smarrimento richiede... = singular subject
• Il deterioramento e lo smarrimento richiedono... = compound subject, so plural verb

This works like English: Deterioration and loss require...

Richiedono is the 3rd person plural, present indicative of richiedere.

So the verb is conjugated like this in the present:

• io richiedo
• tu richiedi
• lui/lei richiede
• noi richiediamo
• voi richiedete
• loro richiedono

Here it matches the plural subject il deterioramento e lo smarrimento.

Here it means to require / to necessitate.

Richiedere can mean both, depending on context:

• Richiedo un duplicato. = I request a duplicate.
• Il deterioramento richiede una nuova emissione. = Deterioration requires a new issuance / reissue.

So in this sentence, the subject is not doing the requesting. It is creating a necessity.

Italian often uses the definite article with nouns in a general or formal sense, especially in administrative language.

So where English may say:

• Deterioration and loss require...

Italian very naturally says:

• Il deterioramento e lo smarrimento richiedono...

This sounds especially normal in formal notices, regulations, and bureaucratic language.

In this sentence, you should keep the second article: il deterioramento e lo smarrimento.

That is because:

1. smarrimento needs lo, not il
2. Repeating the article is the normal and clear choice here

So il deterioramento e smarrimento would sound incomplete or ungrammatical in standard Italian.

They are related, but not always identical in tone.

• smarrimento is very common in administrative Italian for the loss / misplacement of an item, especially a document, card, ticket, or permit
• perdita is a broader, more general word for loss

In official contexts, smarrimento often sounds more natural for something that has gone missing and can no longer be found.

So with documents, badges, cards, etc., smarrimento is extremely common.

It does literally mean emission, but in bureaucratic or administrative Italian it can also mean issuance or issuing, especially of a document, card, ticket, certificate, and so on.

So una nuova emissione here means something like:

• a new issuance
• a replacement issuance
• a reissue

This is one of those cases where the most natural English translation depends on the document or object being discussed.

Because the article is not directly in front of the vowel-starting noun.

Italian uses un' only when una is immediately followed by a feminine singular noun beginning with a vowel:

• un'emissione

But here there is an adjective in between:

• una nuova emissione

So no elision happens. The correct form is una, not un'.

Because many common adjectives in Italian, including nuovo, often come before the noun in ordinary usage.

So:

• una nuova emissione = the normal, natural phrasing

If you put the adjective after the noun:

• un'emissione nuova

it would sound more marked, more contrastive, or less idiomatic in this kind of formal sentence.

So una nuova emissione is the expected choice.

Not necessarily.

In formal or administrative Italian, two situations can be listed with e to show that both are cases that lead to the same result. It does not always mean they must happen at the same time.

So the idea is:

• deterioration requires a new issuance
• loss requires a new issuance

In English, this is often expressed with or, but Italian may still use e when listing conditions in a general way.

If someone wanted to make the either/or idea especially explicit, they might also write:

• In caso di deterioramento o smarrimento...

But the original sentence is still understandable and normal in formal style.