Interestingly this doesn’t see to be a violation of his freedom of speech. The order is simply that he must share it with the government, not that he can’t say it, AFAICT.
But it can affect his supervised release seemingly.
The fourteenth amendment says that rights can be taken away for "rebellion, or other crime". The courts have upheld this, which is why most felons in the USA cannot vote.
So, it's a conditional right, not a fundamental right.
It seems unnecessary to impose this requirement, when the lyrics would eventually be public anyway.
It’s also counterproductive, as it opens the government up to many more avenues of legal attack than simply warning him that publishing violent lyrics may cause an adjustment in his supervised release terms.
I’d love to see the legal justification for applying this prior restraint. Seems like classic overreach, although I doubt the government will see real consequences beyond having their conditions dialed back to where they should have been anyway.
So, it's a conditional right, not a fundamental right.