Is it permissible to lend a computer to one's brother when it is highly probable that he will use it for both permissible and impermissible matters, and is it obligatory to disconnect the internet from it?

It is not forbidden for you to lend the device and enable access to the internet. If the borrower does something forbidden without your knowledge, the sin is on him, not on you. However, if you strongly suspect that he will disobey God by using it, then it becomes forbidden for you to lend it.