היום לא בא לה לבשל, אז היא קונה פיצה.

בא ל־ is a very common Hebrew expression meaning something like to feel like / to be in the mood to.

So לא בא לה לבשל means she doesn’t feel like cooking.

It is less direct than היא לא רוצה לבשל, which means she doesn’t want to cook.
Those are close in meaning, but not always identical:

• לא רוצה = does not want to
• לא בא לה = does not feel like it / is not in the mood

In everyday spoken Hebrew, בא לי / בא לך / בא לו / בא לה is extremely common.

Because in this expression, בא is usually used in a fixed, idiomatic way, even when talking about a woman.

So speakers commonly say:

• בא לי
• בא לך
• בא לו
• בא לה

Even though היא is feminine, the idiom normally stays בא in everyday speech.

You may sometimes hear more formally matched agreement in other contexts, but with this expression, בא ל־ is the standard colloquial pattern.

לה means to her.

In the pattern בא ל־מישהו, the ל־ part marks the person who has the feeling or desire.

So:

• בא לי = I feel like
• בא לך = you feel like
• בא לו = he feels like
• בא לה = she feels like

In your sentence, לא בא לה לבשל literally works like it doesn’t come to her to cook, but the natural meaning is she doesn’t feel like cooking.

Because the expression uses the preposition ל־ meaning to.

The pronoun ה here is the shortened form attached to the preposition:

• ל + ה = לה = to her

Hebrew often attaches prepositions directly to pronouns:

• לי = to me
• לך = to you
• לו = to him
• לה = to her

So בא לה is literally comes to her, idiomatically she feels like.

Because after בא ל־ you normally use the infinitive to say what someone feels like doing.

So the pattern is:

• בא לי לאכול = I feel like eating
• בא לה לישון = she feels like sleeping
• לא בא לנו לצאת = we don’t feel like going out

Here:

• לבשל = to cook

So לא בא לה לבשל = she doesn’t feel like cooking.

Hebrew often uses the present tense for actions happening now, around now, or in a current situation.

In this sentence:

• היום = today
• לא בא לה לבשל = today she doesn’t feel like cooking
• היא קונה פיצה = so she’s buying pizza / she buys pizza

In English, we often prefer is buying here, but Hebrew commonly just uses the present form קונה.

So Hebrew present tense can correspond to English:

• simple present
• present progressive

depending on context.

Yes. Hebrew present tense forms like קונה can mean either:

• buys
• is buying

The context tells you which one sounds natural.

In this sentence, because it is about what she is doing today as a result of not feeling like cooking, English would often translate it as she’s buying pizza. But the Hebrew form itself is just the normal present tense.

Because את is only used before a definite direct object.

Compare:

• היא קונה פיצה = she is buying a pizza / pizza
• היא קונה את הפיצה = she is buying the pizza

Here פיצה is indefinite, so there is no את.

That is a very common thing learners ask about:
את does not mean the object by itself; it marks a direct object when that object is definite.

Here אז means so.

It can also mean then, depending on context.

In this sentence it connects the two ideas:

• today she doesn’t feel like cooking,
• so she buys pizza.

So אז can be a simple result connector in everyday Hebrew.

Hebrew often places time expressions near the beginning of the sentence to set the scene.

So:

• היום לא בא לה לבשל = Today, she doesn’t feel like cooking

This is very natural word order. Hebrew is fairly flexible, but starting with a time word like היום, מחר, or עכשיו is extremely common.

A simple pronunciation guide is:

ha-YOM lo BA la le-va-SHEL, az hi ko-NA PIT-sa

A few notes:

• היום = ha-YOM
• בא = ba
• לה = la
• לבשל = le-va-SHEL
• היא = hi
• קונה = ko-NA
• פיצה = PIT-sa

The main stress is usually on the last syllable in words like:

• לבשל
• קונה
• פיצה

Yes. The structure works the same way with many time expressions.

For example:

• מחר לא בא לה לבשל, אז היא קונה פיצה.
  Tomorrow she doesn’t feel like cooking, so she buys pizza.

• הערב לא בא לה לבשל, אז היא קונה פיצה.
  This evening she doesn’t feel like cooking, so she buys pizza.

• עכשיו לא בא לה לבשל.
  Right now she doesn’t feel like cooking.

So once you know the pattern לא בא לה + infinitive, you can use it very productively.

It is definitely more natural in everyday spoken Hebrew, especially because of לא בא לה.

A more formal or neutral way to express a similar idea would be:

• היום היא לא רוצה לבשל, אז היא קונה פיצה.

That said, your original sentence is extremely natural and common in conversation. If you want to sound like real spoken Hebrew, this is a very useful pattern to learn.