A lyre was a hand-held stringed instrument, played by plucking or strumming its strings.
A noted lyre player at the time of Caesar Nero was Maximus Pettulian of Corinth. The First Doctor once impersonated Pettulian to get into into Nero's court with Vicki. To make the impersonation successful, he had to play the lyre with Nero and his courtiers in the audience.
However, not being able to actually play the device, the Doctor only mimed striking the chords. Because Pettulian's reputation was so great, and Nero, who fancied himself an expert lyre player, did not want to appear foolish, the Doctor was able to convince Nero that he was playing with exceptional subtlety.