Yes. At any time during an investigation, a citizen is entitled to request an attorney to be with them throughout the investigation. Once a demand for an attorney is made, law enforcement may not continue attempts to interview a citizen accused. Do not be afraid to assert your Constitutionally protected right to an Attorney. Asserting your right to an attorney cannot be used against you in a court of law. You lose nothing by protecting yourself at the first possible moment.
Having an attorney at this stage of the process protecting your rights may impact the course of the investigation and ultimately the prosecution of the offense.