NSW Can ex criminal become lawyers

Depends on the offence(s).

If it was a long time ago, or didn't involve dishonesty offences

becoming a lawyer criminal record - Google Search

Reading through the first three results should provide you with your answer. If you are still unclear about a specific conviction, then feel free to come back here and seek further advice. Be advised however, that if you seek further opinion relating to a specific conviction, it is unlikey that anyone would be able to help unless you state what the actual charge was.

You can get an ‘Early declaration of suitability’ from most Legal Practice Boards throughout the Country where the relevant board decides whether the offence(s) would prevent you from being considered a ‘fit and proper person’ before undertaking your studies (if that is your concern).