Is Hajj obligatory for someone who performed Umrah before Dhu al-Hijjah, even though he had previously performed Hajj?

Hajj is obligatory only once in a lifetime, based on the Prophet's (peace be upon him) saying: "Hajj is once; whoever performs it more than that, it is a voluntary act." Since you have performed Hajj, it is not obligatory for you to do so again. Naming Shawwal, Dhul-Qa'dah, and Dhul-Hijjah as the months of Hajj does not mean that Hajj becomes obligatory for someone who performs Umrah during them; rather, it means that Hajj must take place within these months. There is nothing [obligatory] upon the mutamatti' (one who performs Umrah and then Hajj) who performed Umrah and then returned to his country without performing Hajj, unless he had made a vow to perform Hajj in that specific year.