The First Amendment allows government to impose “time, place, and manner” restrictions on protected speech. So if you give a speech protected by the First Amendment, the government can still regulate your use of sound amplification, including things like regulating noise levels at night or in residential areas. If you assemble in an assembly protected by the First Amendment, the government may still enforce fire code restrictions like occupancy limits in a building or weight limits on a platform, or even permitting requirements for all of the above.
The First Amendment also distinguishes between public forum, limited public forums, and nonpublic forums. The government must allow people to use things like theaters and stages for First Amendment speech and expression, but doesn’t have to do things like let protestors onto restricted military bases to protest.
Permitting is one way to regulate time, place, and manner. Also, it’s a way to prevent double booking. A city-run community theater might allow for one church to hold services on Sunday, and a first come first serve policy might cause the city to deny access to another church that wants to use the exact same place at the exact same time.
So a specific lawn on a public university campus might require permitting in a way that complies with the First Amendment, if the permitting is used to:
Prevent overcrowding beyond safe limits
Prevent excessive wear and tear on the grass/landscaping
Prevent multiple groups holding incompatible activities in the same space
Prevent interference with actual governmental functions (e.g., not disrupting classes being held)
Keep the First Amendment protected activity within the actual zones where that is permitted
People can and do engage in First Amendment protected activity outside of those lines, of course. Sometimes the point of a protest is to break the law: civil rights sit ins, marches on specific streets, etc. But the organizers and the governmental authority generally need to work at defining those lines clearly, so that any decision to break the law is conscious and planned.