ميزانية الأسرة صعبة، لا سيما الدين.

Because Arabic normally leaves out the present-tense verb to be.

So:

• ميزانية الأسرة = the family's budget
• صعبة = difficult / hard / tight

Together, ميزانية الأسرة صعبة literally works as The family's budget [is] difficult/tight.

This kind of sentence is called a nominal sentence in Arabic.

This is an iḍāfa construction, often called the construct phrase.

Structure

• ميزانية = budget
• الأسرة = the family

Put together:

• ميزانية الأسرة = budget of the family = the family's budget

Important iḍāfa rules

• The first noun usually does not take ال here.
• The second noun shows who owns or defines the first noun.
• The whole phrase becomes definite because الأسرة is definite.

So even though ميزانية does not have ال, ميزانية الأسرة still means the family's budget, not just a family budget.

Because ميزانية is a feminine singular noun, and adjectives must agree with the noun they describe.

So:

• ميزانية = feminine singular
• صعبة = feminine singular adjective

If the noun were masculine, you would expect صعب instead.

This is grammatical gender, not biological gender.

لا سيما is a fixed expression meaning:

• especially
• particularly
• above all

So:

• لا سيما الدين = especially the debt

It singles out one item from the general situation just mentioned.

In this sentence, the general idea is that the family's budget is difficult, and debt is being highlighted as a major part of that problem.

You can think of it as similar to:

• especially debt
• particularly debt
• debt in particular

Here it means debt.

That is a very common learner question because Arabic script usually leaves out short vowels, so الدين can represent two different words:

• الدَّيْن = debt
• الدِّين = religion

In this sentence, the context is budget, so the meaning must be debt.

So the intended reading here is:

• الدَّيْن = ad-dayn = debt

not

• الدِّين = ad-dīn = religion

Because د is a sun letter.

With sun letters, the ل of ال is not pronounced separately; instead, it assimilates to the next consonant.

So:

• الدَّيْن is pronounced ad-dayn
• not al-dayn

By contrast, in الأسرة, the ال is pronounced normally:

• الأسرة = al-usra

So a helpful pronunciation for the full sentence is:

• mīzāniyyat al-usra ṣaʿba, lā siyyamā ad-dayn

This is a more advanced grammar point.

After لا سيما, Classical and formal Arabic grammar allows more than one analysis, so in fully vowelled Arabic you may see different case endings on the following noun.

That means a word after لا سيما can appear in more than one form in formal grammar discussions.

But in normal modern writing, Arabic usually omits case endings, so you simply see:

• الدين

without any visible final vowel.

For most learners, the important point is just:

• لا سيما + noun = especially + noun

You do not need to master all the case analyses right away to understand the sentence.

Yes. It is understandable and natural enough in Modern Standard Arabic.

Here صعبة does not mean the budget is difficult in a strange literal sense; it suggests that the budget is:

• tight
• strained
• hard to manage

So the phrase gives the idea that the family's financial situation is difficult.

Depending on style, Arabic could also use other expressions, such as:

• ميزانية الأسرة ضيقة
• تعاني الأسرة من ضائقة مالية
• ميزانية الأسرة صعبة، لا سيما بسبب الدَّيْن

But the original sentence is perfectly understandable.

Yes. In Modern Standard Arabic, common alternatives include:

• خصوصًا
• وخاصةً

So these would be similar in meaning:

• ميزانية الأسرة صعبة، خصوصًا الدين
• ميزانية الأسرة صعبة، وخاصةً الدين

A slightly more explicit version would be:

• ميزانية الأسرة صعبة، لا سيما بسبب الدَّيْن
• The family's budget is difficult, especially because of debt

So لا سيما is a formal and useful expression, but not the only option.