"My son wants to be a lawyer."
Translation:Mio figlio vuole diventare avvocato.
Because family members (in the singular and without modifiers) are exceptions and don't use the definite article. http://italian.about.com/library/fare/blfare124a.htm
diventare is to become, but the translation given here is the closest English idiom, and in English you say that you want to be something, not that you want to become something (mostly).
And I just looked at the 'answer' and saw the essere. Apparently they are somewhat interchangeable. I used 'diventare' here and it accepted it quite happily.