" inappropriate lyrics should be banned from the radio "

The "exact" definition of Freedom of Speech may well be the "freedom to speak freely without censorship" [1]. But that is most certainly not the meaning of the First Amendment to the Constitution of the United States. There are a variety of limitations to our Freedom of Speech.

Determining whether or not radio censorship violates the First Amendment, we need to acknowledge that such determinations are an official function of the Judiciary branch. With their interpretive powers, the Courts determine if a law or regulation is unconstitutional.

The most applicable court case here would be FCC V. Pacifica Foundation, 438 U.S. 726, 57 L. Ed. 2d 1073, 98 S. Ct. 3026 (1978) wherein the FCC issued sanctions against a radio station for airing an obscene broadcast [2]. Note that the FCC does not censor, even if it takes punitive actions. Censorship is provided by he broadcasting company itself (which does not violate the First Amendment, as a private entity) as a proactive measure to avoid FCC fines and sanctions.

Until a new case overturns this decision, the FCC's authority to punish broadcasting companies for such content remains valid and, even if this authority was invalidated, private companies would still retain the authority to censor their own broadcasts, as the First Amendment only applies to government entities.

[1] http://en.wikipedia.org...
[2] http://www.ala.org...