Is it permissible for the kaafir to enter the mosque to attend a lecture or a lesson in which there is an invitation to Islam?.
Yes, this is permissible, if we are confident that this kaafir will not disrespect the mosque, because he is entering for a reason, and not to harm or damage the mosque. Similarly it is permissible for a kaafir to enter and stay in the mosque to repair something in the mosque, because this is in the interests of the mosque, so it is also permissible for him to enter to listen to lectures which may be the cause of his being guided. The Prophet (peace and blessings of Allaah be upon him) tied up Thumaamah ibn Athaal in the mosque [when he was a prisoner of war, before he became Muslim]. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him).