Yes, liberi means free children. Pueri is the generic word. Gaffiot quotes namely Cicero: liber, qui de matre libera, liber est. The same Gaffiot, under liberi gives an even more restrictive definition of free boys (not girls).
What is the meaning of Liberi?
Italian: patronymic or plural form of the personal name Libero from Latin liber 'free'.
What does Liberi in Latin mean?
līberī m pl (genitive līberōrum); second declension, (plurale tantum) children. offspring.
Why is it called Liberi?
The local tribes continually attacked the new colony and in 1824, the settlers built fortifications for protection. In that same year, the settlement was named Liberia and its capital Monrovia, in honor of President James Monroe who had procured more U.S. Government money for the project.