היא יצאה מהבית בלי שאכלה ארוחת צהריים, ולכן באמצע האימון כאבה לה הבטן.

Because the subject is היא (she), so the verb has to be feminine singular in the past tense.

• הוא יצא = he went out
• היא יצאה = she went out

In Hebrew past tense, verbs agree with the subject in gender and number.

מהבית means from the house / from home.

It is made of:

• מ־ = from
• הבית = the house / the home

So:

• מ + הבית → מהבית

This is the normal modern Hebrew way to say from the house.
The longer form מן הבית also exists, but it is more formal or literary. In everyday Hebrew, מהבית is much more natural.

Both are possible in Hebrew, but they are not exactly the same.

• בלי לאכול ארוחת צהריים = without eating lunch
• בלי שאכלה ארוחת צהריים = without having eaten lunch / without the fact that she ate lunch

In this sentence, בלי ש־ introduces a full clause with its own verb: אכלה.
That makes the action feel a little more explicit and complete.

So:

• בלי לאכול
  • infinitive
• בלי ש...
  • conjugated verb

Both are common, but בלי שאכלה sounds very natural here.

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

Here, אכלה already means she ate, because it is feminine singular past. So adding היא would usually be unnecessary.

• שאכלה = that she ate
• שהיא אכלה = that she ate

The second version is possible, but usually less natural unless you want special emphasis.

ארוחת צהריים means lunch.

Literally, it is:

• ארוחה = meal
• ארוחת = meal of ... / meal in the construct form
• צהריים = noon / midday

So ארוחת צהריים literally means the meal of noon, which is the normal Hebrew expression for lunch.

This is a construct phrase in Hebrew, where the first noun changes form:

• ארוחה → ארוחת

Because צהריים is one of those Hebrew time words that has a plural-looking form but refers to a single time of day.

Compare:

• בוקר = morning
• ערב = evening
• צהריים = noon / midday / afternoon
• שמים = sky
• מים = water

So even though צהריים looks plural, in ארוחת צהריים it simply means lunch.

ולכן means and therefore, so, or and as a result.

It is made of:

• ו־ = and
• לכן = therefore / therefore so

In Hebrew, it is very common to attach ו־ directly to the next word. So ולכן is just one written word, but it really contains two parts.

Literally, it means in the middle of the training/workout.

Parts:

• ב־ = in
• אמצע = middle
• האימון = the training / the workout

So:

• באמצע = in the middle of
• באמצע האימון = in the middle of the workout

אימון can mean training, practice, or workout, depending on context.

Hebrew often expresses physical sensations with a structure like:

• כאב לי הראש = my head hurt / I had a headache
• כואבת לי הבטן = my stomach hurts
• כאבה לה הבטן = her stomach hurt

Here, לה literally means to her, but in natural English we translate it as her:

• כאבה = hurt (feminine past)
• לה = to her
• הבטן = the stomach

So the structure is more like the stomach hurt to her, even though that sounds unnatural in English.

This is a very common Hebrew pattern with body parts and feelings.

Because הבטן is a feminine noun in Hebrew.

So the verb must agree with הבטן:

• כאב הראש = the head hurt
• כאבה הבטן = the stomach hurt

Even though the person affected is her, the verb agrees with הבטן, not with לה.

That is very normal in Hebrew. With body parts, Hebrew often uses the definite noun plus an indirect pronoun:

• כואב לי הראש = my head hurts
• כואבת לה הבטן = her stomach hurts

So instead of saying her stomach, Hebrew often says something closer to the stomach hurts to her.

That is why הבטן is definite here.

No, Hebrew word order is somewhat flexible here.

You could also hear:

• הבטן כאבה לה
• כאבה לה הבטן

Both are grammatical.

The version in your sentence, כאבה לה הבטן, is perfectly natural and puts the verb first, which is very common in Hebrew narrative style.

The main thing that stays the same is the grammatical relationship:

• כאבה agrees with הבטן
• לה marks the person experiencing the pain