Daughter of Latinus, betrothed to Turnus, King of the Rutuli.
When Æneas landed in Italy, Latinus made an alliance with the Trojan
hero, and promised to give him Lavinia to wife. This brought on a war
between Turnus and Æneas, which was decided by single combat, in which
Æneas was victor. (Virgil Æneid.)
The daughter of Titus Andronicus, bride of Bassianus, brother of
the Emperor of Rome. Being grossly abused by Chiron and Demetrius, sons
of Tamora, Queen of the Goths, the savage wantons cut off her hands and
pluck out her tongue, that she may not reveal their names Lavinia,
guiding a stick with her stumps, makes her tale known to her father and
brothers; whereupon Titus murders the two Moorish princes and serves
their heads in a pasty to their mother, whom he afterwards slays,
together with the Emperor Saturninus her husband. (Titus Andronicus,
a play published with those of Shakespeare.)
In the play the word is accented Andronicus not Andronicus.
Italy; so called from Lavinia, daughter of Latinus and wife of
Ænes. Ænes built a town which he called Lavinium, capital of Latium.
From the rich Lavinian shore
I your market coine to store.
A well-known Gloe
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Lavinia from Infoplease: