What is the ruling on providing internet access to non-Muslims and Muslims, knowing that it is used for unlawful acts? Is it permissible to cut off the service, despite causing harm to the institution and lying to justify it?

If your provision of a service that could be used for forbidden matters was done out of ignorance, then there is no sin upon you. However, if you knew or strongly believed that it would be used for forbidden matters and you proceeded with it, then you must repent to Allah and resolve not to return to it.

In all cases, you must remove this evil to the best of your ability, even if by lying, because it is permissible to deter others from evil and achieve a praiseworthy legal purpose, and this applies equally to Muslims and non-Muslims, as it is not permissible to assist a non-Muslim in disobedience.