The correct option is A, i.e., the State is bound to provide a lawyer as it is a matter of right.

The legal principle of "free legal aid" means that every person, regardless of their economic or social status, has the right to access legal representation and receive legal aid if they cannot afford it. This principle is enshrined in Article 39A of the Constitution of India, which directs the State to provide free legal aid to ensure that justice is not denied to any person due to economic or other disabilities.

In the factual situation presented, the lady who has to file a suit for maintenance against her husband does not have the resources to engage a lawyer. In such a situation, she can approach the State to engage an advocate at State expenses, as she has the right to free legal aid.

Therefore, the State is bound to provide her with a lawyer, and cannot deny her on the grounds of unavailability of a lawyer or lack of finance. The right to free legal aid is an essential component of access to justice, and the State has a duty to ensure that this right is respected and upheld for all its citizens.