Does the lecture hall of the Islamic center take the ruling of the original mosque, such that it is permissible to perform the Qiyam prayer in congregation there outside of Ramadan, by analogy with the rule "the تابع follows the متبوع" (the subordinate follows the principal), or is it considered separate by analogy with the houses of the Prophet, peace be upon him, that were adjacent to the mosque?

Performing Qiyam (definition) al-Layl (night prayers) in congregation is a Sunnah (definition) during Ramadan (definition). It is permissible to perform it in congregation occasionally outside of Ramadan, provided it is not adopted as a regular habit or a fixed Sunnah. This is because regular congregational prayer is not legislated for acts that do not have a prescribed regular congregation, such as Qiyam al-Layl. As for habitually performing it in a regular congregation, that is a reprehensible innovation (bid‘ah makroohah). The criterion for permissibility is not the place, but rather the continuity or lack thereof.