Is hunting in a lake owned by the state and leased for private exploitation considered theft?

This lake is among the permissible things that the state is not allowed to rent out or impose fees for fishing in it or for accessing its shores, unless there is a clear public interest that benefits all Muslims, and not just a specific group, while observing the Shariah guidelines of preventing nudity and indecency. In this case, it is not permissible for anyone other than the renter to fish from it without his permission, and whoever does so has trespassed and acted wrongly. However, their action is not considered theft due to the absence of the conditions for theft.