It is not permissible to give it for the intention of performing hajj even if he was needy.
We give him the zakat because he is needy and not to perform hajj.
Allah says: “As-Sadaqât (here it means Zakât) are only for the Fuqarâ’ (poor), and Al-Masâkin (the poor) and those employed to collect (the funds), and to attract the hearts of those who have been inclined (towards Islâm); and to free the captives, and for those in debt, and for Allâh’s Cause (i.e. for Mujâhidûn – those fighting in a holy battle), and for the wayfarer (a traveler who is cut off from everything); a duty imposed by Allâh. And Allâh is All-Knower, All-Wise.”
This is in the people who started their journey and then lost their money and were unable to go back. This is different from a person who wants to initiate travelling for hajj and doesn’t have the means to do so. One of the main requirements of Hajj is to be able financially.