Note to JULIUS CAESAR, 4.3.239, 'thy instrument'
In ancient Rome the premier stringed instrument, the one most used by singers to accompany themselves (as the guitar is used today) was the cithara:
Lucius (John Hardy) with a cithara, Brutus (James Mason) looking on,
in the
1953 movie starring Marlon Brando and James Mason
However, since Shakespeare seems to think that Rome had Elizabethan doublets, clocks and chimneys, I'm guessing that he would also would have seen nothing wrong with Lucius playing the most popular stringed instrument of his own time, the lute:

"The Lute Player"
by
Michelangelo Merisi da Caravaggio.