Suetonius tells us that he won the award for lyre-playing, but given that it was at an event that he established and called the Neronia, I think we have to assume that there may have been some political pressure on the judges (ex-consuls, Suetonius tells us). There are also other similar references -- his holding the Neronia again before the appointed time and being asked to perform personally -- again, we need to consider that this may not be an honest artistic opinion. Likewise, we shouldn't immediately assume that he was bad when Vindex called him a terrible lyre-player, since it is clear that he was attempting to ridicule Nero or goad him into behaving rashly during his rebellion, and so again, the insult is likely to be more about politics than music.

Suetonius does make a passing mention of Nero's music being syndicated, more or less -- a collection of his music which Suetonius reports was called the "Dominicus" (or Lord's/Master's book) existed, such that it could be pulled out by a musician performing for Vitellius, who made a show of honouring Nero to legitimize his own rule as being an avenger of Nero, who was the last emperor from the original Claudian dynasty.

I have a side question: was the lyre a common instrument to play in Rome at the time?