The ruling for lying on official documents to make hajj
Some people lie on the official documents that they are asked to submit and give false information for the sake of traveling for hajj. For instance, they may falsely claim that they have not previously performed hajj. Is lying in such a case permissible? And is it permissible for a driver, for instance, to falsely claim that he has previously performed hajj to be able to work as a driver during the hajj season? And is it permissible to stay behind in the Sacred land after the hajj season to work and worship God?
It is established in Islamic law that it is obligatory to defer to the rulings of those vested with authority provided their rulings are not unlawful and there is no consensus on their unlawfulness. Ibn 'Umar (may God be pleased with him) narrated that the Prophet said, "A Muslim must hear and obey those vested with authority concerning what he likes and what he does not like, unless he is commanded to do a wrong action. Otherwise, he must not obey" [Recorded by Bukhari, Muslim, At-Tirmidhi, Ibn Majah, Al-Nisa`i and Abu Dawud].
A ruler is entitled to pass laws that, in his opinion, achieve the interests of his people. Whoever enters a country must conform to its laws and it is prohibited to violate them.
It is prohibited to lie in all cases, except those deemed exceptions by Islamic law. Examples of such cases are included in the hadith narrated by Asmaa` Bint Yazid who narrated that the Prophet said, "It is not valid to lie except in three situations: when a man talks to his wife (to please her), to settle disagreements between people, and in war" [Recorded by Ibn Abu Shaybah, at-Tirmidhi, and others].
Based on this, the types of lies mentioned in the question are from among what is unlawful and are not included among the exceptions made and deemed permissible by Islamic law.
It is impermissible to deceive authorities by giving false information, whether for the purpose of traveling to perform hajj or to achieve any other interest in one's country or in one's country of destination. It is likewise impermissible to extend one's stay after completing the rites of hajj if the ruler forbids this.