Is it permissible for a non-Muslim to enter a mosque to attend a lecture or lesson that involves teaching and an invitation to Islam?

Yes, it is permissible for a non-Muslim to enter the mosque to listen to lectures, which may be a cause for their guidance, provided there is no fear of them defiling the mosque. This is analogous to the permissibility of their entry to repair something within it. The Prophet, peace and blessings be upon him, also tied Thumamah ibn Uthal in the mosque.