Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- It is surely allowed for a Muslim woman to join public life introducing lectures and other activities either on the Internet or offline.
2- Indeed, the Muslim Ummah is in bad need of every single effort that shows and spreads the real and good image of Islam.
Responding to your question, Imam Dr. Wael Shehab, the Imam of Toronto Masjid and the Fatwa section of IslamOnline.net (English Website), sates:
Of course, it’s acceptable for Muslim sisters to engage in the public life and promote Islam’s message and values. Our Islamic history bears witness to the fact that great Muslim women had been among the leading scholars in every branch of knowledge, including the Islamic sciences such as Hadith, Fiqh, Tafseer, etc.
So, sisters can have lectures online, and offline of course, in all available good channels, including Youtube, to promote Islamic values and morals as long as they follow Islamic ethics in this regard.
Allah Almighty knows best.