All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
We have previously underlined in several fatwas that it is impermissible to hold more than one Friday prayer in the same town unless there is a need or necessity, such as the long distance to the masjid, or if the masjid is not spacious enough to accommodate all the worshippers, or out of fear of Fitnah (temptation/tribulation) or similar reasons which justify holding two or more Friday prayers.
The Kuwaiti Encyclopedia of Fiqh reads:
"According to the majority of the scholars, it is impermissible to hold two Friday prayers in one town except for a necessity, such as if the mosque is too small to accommodate all the worshippers, because the Prophet, sallallaahu ‘alayhi wa sallam, and the Rightly-Guided Caliphs after him held only one Friday prayer ... The majority of the scholars held that it is impermissible to hold multiple Friday prayers in general, with slight differences of opinion among them with regards to the criteria of the place where holding multiple Friday prayers is impermissible. According to Ash-Shaafiʻi, Ahmad, and the stronger opinion reported from Maalik, it is impermissible to hold multiple Friday prayers in the same town, regardless of whether it is big or small, unless there is a need for that. This was also the opinion of Abu Haneefah, and it was held as valid by Ibn ʻAabdeen ... A fatwa was issued based on this opinion. They said: it is because the rationale behind holding the Friday prayer is that the Muslims gather and meet. Scattering in several mosques without a need contradicts this rationale. Also, it was not reported from any Companion or Taabiʻi (generation following that of the Companions) that it is permissible to hold multiple Friday prayers in the same place (without a need)..." [Abridged]
As long as the Friday prayer is held in your town within its time – even if it is delayed but held before its time expires – it is impermissible for you to hold another Friday prayer merely because you have a lesson at the beginning of its time, especially given that you find enough time to rest after the lesson; two hours, as you mentioned. So it is impermissible for you to hold another Friday prayer, and you are obliged to attend the Friday prayer with the main congregation in the masjid.
Allah knows best.