اگر مادرم و خواهرت بیایند، لازم است که بشقاب و قاشق بیاوریم.

After اگر, Persian often uses the present subjunctive when talking about a future or possible condition.

So:

• اگر ... بیایند = if they come
• می‌آیند = they come / they are coming

Here, بیایند is the natural choice because the sentence is describing a condition, not stating a plain fact.

Because the subject is compound: مادرم و خواهرت = my mother and your sister.

When two people are joined by و (and), Persian normally uses a plural verb. That is why the verb is:

• بیایند = they come

If there were only one person, it would be:

• بیاید = he/she comes

Persian often shows possession by adding a suffix directly to the noun.

• مادر = mother

• مادرم = my mother

• خواهر = sister
• خواهرت = your sister

So the endings are doing the work of English my and your.

-ت is the singular informal or familiar your.

So:

• خواهرت = your sister addressed to one person informally

If you wanted a more formal or plural your, you would usually say:

• خواهرتان = your sister (formal or plural)

لازم است literally means it is necessary or it is needed.

The که introduces the following clause, like English that:

• لازم است که ... = it is necessary that ...

In many cases, که is optional here, so this is also possible:

• لازم است بشقاب و قاشق بیاوریم

Including که can sound a little more explicit or slightly more formal.

Because after expressions like لازم است (it is necessary), Persian normally uses the subjunctive.

• بیاوریم = that we bring

It comes from آوردن (to bring), and the ending -یم shows we.

So the structure is:

• لازم است که ... بیاوریم = it is necessary that we bring ...

Persian often leaves out subject pronouns when the verb already makes the subject clear.

Here, بیاوریم already tells you the subject is we because of the ending -یم.

So:

• بیاوریم already means we bring / that we bring

You could add ما for emphasis, but it is not required.

In Persian, bare nouns are often used for non-specific things, even when English would translate them as plurals.

So:

• بشقاب و قاشق بیاوریم

can naturally mean:

• bring plates and spoons

Persian does not always mark plural when the exact number is not important. If you wanted to make the plural more explicit, you could say:

• بشقاب‌ها و قاشق‌ها

Because را usually marks a specific or definite direct object.

Here, بشقاب و قاشق means something like some plates and spoons or plates and spoons in general, not a specific known set. So را is not needed.

Compare:

• بشقاب و قاشق بیاوریم = bring plates and spoons
• بشقاب و قاشق را بیاوریم = bring the plates and spoons

Because Persian is usually a subject-object-verb language.

That means the verb often comes at the end of the clause. So the normal order is:

• object first: بشقاب و قاشق
• verb last: بیاوریم

This is why بشقاب و قاشق بیاوریم sounds natural in Persian.