That's the only way to say it in Latin, since there are no third person possessive pronouns in Latin equivalent to the English words "his", "her", "its", and "their". In other words, you have to use the genitive of is,ea,id, i.e. eius (his,her,its) in the singular and eorum/earum (their) in the plural. There is a third person reflexive possessive pronoun suus,-a,-um, which is fully declined, but that would mean "his/her/its/their own" and thus wouldn't work in that sentence from Lingua Latina.
Actually, there is one other way to render that last sentence. You could use the dative of possession, which uses the dative in tandem with the verb esse to indicate that the subject belongs to the dative noun: i.e. Dominus eis est Iulius. An equivalent literal translation into English would be "The lord to them is Julius", but that's obviously ungrammatical English.
Ex mala malo
bono malo uesci
quam ex bona malo
malo malo malo.