When can the plaintiff's lawyer intervene in a criminal case?

You should be talking about the lawyer who represents the plaintiff in the criminal incidental civil action. Article 40 of the Criminal Procedure Law stipulates: "The victims of public prosecution cases and their legal representatives or close relatives, and the parties involved in incidental civil actions and their legal representatives have the right to entrust agents from the date when the case is transferred for examination and prosecution. The private prosecutor and his legal representative in a case of private prosecution, and the parties to an incidental civil action and their legal representatives have the right to entrust an agent at any time. " The "date when the case was transferred for examination and prosecution" here refers to the date when the case was transferred to the people's procuratorate for examination and prosecution after the investigation by the public security organ ended.