The Luccini were allies of the Vongola family.
The family was composed of Mr Luccini, his son Stefano and his wife Elisa, then their twin sons Luca and Arina.
Stefano and Elisa were killed by some Vongola rival, together with the Belfiore and the Coleandro.
The two children were assigned to two different families.
Luca was adopted by a newly married couple while Arina was taken into custody by Vongola Decimo.
Mr. Luccini, who was very old, died a few years later.

Vongola no Uta

Decimo has discovered that Lhumor Corp. killed Stefano and Elisa, Arina tried to forget what happened while Nozomi decided to avenge them.