What does lār familiāris mean in Latin?

lār familiāris, a noun, means “a household deity”.

What is the genitive of lār familiāris?

The genitive singular is laris familiāris. lār familiāris is third declension.

nounthird declension

lār familiāris m (genitive laris familiāris)

declension
form	singular	plural
nominative	lār familiāris	larēs familiārēs
genitive	laris familiāris	larum familiārium
dative	larī familiārī	laribus familiāribus
accusative	larem familiārem	larēs familiārīs larēs familiārēs
ablative	lare familiārī	laribus familiāribus
vocative	lār familiāris	larēs familiārēs

See lār (“tutelary deity”), familiāris (“pertaining to a household”).